text stringlengths 81 47k | source stringlengths 59 147 |
|---|---|
Question: <p>Can you guys answer this question regarding part (c)? I am confused of what he means.</p>
<p>A deck of <span class="math-container">$52$</span> cards is mixed well, and <span class="math-container">$5$</span> cards are dealt.
(a) It can be shown that (disregarding the order in which the cards are dealt) th... | https://math.stackexchange.com/questions/1447262/probability-of-hand-having-cards-from-exactly-two-hands |
Question: <p>Given a sample (the scope is 72 elements) with mode=54 mean=55,7 median=54,5. The 73th value of the extended sample is 56. What can I say about the mode, median and mean of the extended sample?</p>
<p>Well, the updated mean is easy to calculate. </p>
<p>To make a statement about the median I know the 36t... | https://math.stackexchange.com/questions/1484493/extended-sample-mode-median-mean |
Question: <p>Given a distribution with density
<span class="math-container">$$f(x)=\frac{x}{\theta^2}\exp(\frac{-x}{\theta})$$</span>
How do I find the Maximum Likelihood Estimator of <span class="math-container">$\log(θ +7)$</span> ?</p>
<p>I have found the MLE of <span class="math-container">$\theta$</span> as
<sp... | https://math.stackexchange.com/questions/2979184/finding-mle-of-a-distribution-density-and-derive-a-new-mle-based-off-of-the-par |
Question: <p>I've found different formulas for the Gamma distribution, one where Gamma(alpha, lambda) has an expected value of alpha/lambda due to the Gamma distribution turning into the following image: <a href="https://prnt.sc/lcq5zq" rel="nofollow noreferrer">https://prnt.sc/lcq5zq</a>. However, in other sites I see... | https://math.stackexchange.com/questions/2979196/whats-the-difference-between-gammaalpha-lambda-and-gammaalpha-beta |
Question: <p>I am sorry for the poor quality of this question: For <span class="math-container">$\Gamma(\alpha,\beta)$</span> random variables, why do we assume <span class="math-container">$\alpha>0$</span> and <span class="math-container">$\beta>0$</span>?</p>
Answer: <p>The gamma density is the following, for... | https://math.stackexchange.com/questions/4170608/positive-parameters-for-gamma-random-variables |
Question: <p>I apologize for the title. I am not even sure how to phrase this question per se. I feel like this should be easy and yet I am questioning my thinking. Here's the scenario:</p>
<p>I have two groups. Group A has 50 members. Group B has 400 members. What I want to know is what the calculation would be ... | https://math.stackexchange.com/questions/4176527/basic-math-question-i-think |
Question: <p>In an office of 20 people ther are only 4 salary levels paid :
50 000 (1 person), 42 000 (3 people), 35 000 (6 people), 28 000 (10 people).</p>
<p>I calculate the mean = 33300, the median = 30000 (usd).</p>
<p>But I am not sure which measure of central tendency might be used by the boss who is against a ... | https://math.stackexchange.com/questions/2993373/which-measure-of-central-tendency-might-be-used-by-the-boss-who-is-against-a-pay |
Question: <p>A sample of $40$ women is obtained and their heights in inches and pulse rate in beats per minute are measured. The linear correlation coefficient is $0.221$ and the equation of the regression line is $y = 18.5+0.860x$ where $x$ represents height and $y$ the pulse rate. The mean of the $40$ heights is $62.... | https://math.stackexchange.com/questions/1178005/statistics-regression |
Question: <p>During the log phase of bacterial growth the size of the colony grows exponentially. Let <span class="math-container">$R$</span> be the ratio of the biomass at time 1 hour to the initial biomass. Then <span class="math-container">$R=e^r$</span> where <span class="math-container">$r$</span> is the instantan... | https://math.stackexchange.com/questions/4183246/determining-probability-after-standardizing-for-given-problem |
Question: <p>Imagine a 10 x 5 grid where each square can be either 1 or 0. However, each row (10 squares) must contain five 1's and five 0's. Therefore, each grid (of 50 squares) has twenty five 1's and twenty five 0's but their distribution is somewhat controlled in that each row must contain five of each.</p>
<p>How... | https://math.stackexchange.com/questions/3153176/how-many-possibilities-can-a-10x5-grid-with-somewhat-even-distribution-produce |
Question: <p>I work for a law firm and I want to know whether I can accurately predict our future revenue based on data I've pulled from our SQL Server database. Here is the information that I know based on some queries:</p>
<ol>
<li><p>It takes on average, 333 days from the time we sign up a client until we get a sett... | https://math.stackexchange.com/questions/4186587/how-to-forecast-revenue-with-my-data |
Question: <p>I work on 'real-life data' and to simplify, I have a sample of 10.000 observations of two variables <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> with a categorical variable <span class="math-container">$C$</span> that is either <span class="math-container">$C=0$</span... | https://math.stackexchange.com/questions/4178919/pearson-correlation-over-subsamples-compared-to-the-whole-sample |
Question: <pre><code>Event Trigger Check Interval: 3 minutes
Trigger Chance of Event: 5%
Event Length: 10 minutes
</code></pre>
<p>The above are the 3 variables in this problem. To give it a story, let's say I click a button every <strong>3 minutes</strong>, with the first click at minute 3 (not 0). On click, there i... | https://math.stackexchange.com/questions/4187831/event-uptime-over-a-course-of-time |
Question: <p>"Consider the mean combined SAT score for high school seniors is 1500, and the standard deviation is 250. Calculate the percentage of students who scored at the following levels"...</p>
<p>Can anyone figure out what this question is asking for? I can find a Z-score then a corresponding probability but I d... | https://math.stackexchange.com/questions/1883202/consider-the-mean-combined-sat-score-for-high-school-seniors-is-1500 |
Question: <p>The relative error is defined by the simple formula:</p>
<p>$$\text{Rel. Error} = \frac{|v_\text{approx}-v_\text{analytical}|}{v_\text{analytical}}$$</p>
<p>but what if the theoretical value $v_\text{analytical}$ should be $0$? then our relative error is undefined.... this is also quite a common occurs. ... | https://math.stackexchange.com/questions/2502932/what-if-the-relative-error-is-undefined |
Question: <p>My textbook mentions this:</p>
<p>"To construct a histogram, first decide how many bars or intervals, also called classes, represent the data. Many
histograms consist of five to 15 bars or classes for clarity. The number of bars needs to be chosen. Choose a starting point
for the first interval to be less... | https://math.stackexchange.com/questions/3211937/when-creating-histograms-what-is-wrong-with-data-values-falling-on-boundaries |
Question: <p>I cannot seem to find a proof that $f(\mathbf{\beta}) = \left\lVert \mathbf{y}-\mathbf{X} \mathbf{\beta} \right\rVert^2$ is an ellipsoid, centered at the OLS solution $\hat{\beta}$. Can anyone show how to convert it to the quadratic form of a general ellipsoid, i.e. $(\beta - \hat{\beta})^T \mathbf{A} (\be... | https://math.stackexchange.com/questions/2909077/proof-that-loss-function-for-linear-regression-is-an-ellipsoid |
Question: <blockquote>
<p>If <span class="math-container">$U$</span> and <span class="math-container">$X$</span> are random variables such that <span class="math-container">$E(U|X)=0$</span>, then <span class="math-container">$E(U)=0$</span>.</p>
</blockquote>
<p>Really? how to prove?</p>
Answer: <p><span class="ma... | https://math.stackexchange.com/questions/2924578/if-eux-0-then-eu-0 |
Question: <p>Let <span class="math-container">$X_1, X_2, \ldots, X_n$</span> be i.i.d exponential random variables with parameter <span class="math-container">$\lambda$</span>, where the form of the distribution for each <span class="math-container">$x_i$</span> is</p>
<p><span class="math-container">$$f(x_i) =\lambda... | https://math.stackexchange.com/questions/2928389/expectation-of-mle-for-exponential-r-v-s-with-censoring |
Question: <p>This questions was proposed by our statistics teacher as home work.</p>
<p>I have been looking for any reasonable explanation but so far I am getting more and more confused differentiating between the two concepts.</p>
<p>Could someone please clarify them for me?</p>
Answer: <p>If A and B are independen... | https://math.stackexchange.com/questions/2941568/is-there-any-relation-between-a-independece-of-a-event-and-a-mutual-exclusive-ev |
Question: <p>There are two groups of people, target and neutral</p>
<p>There are two group of events X and others</p>
<p>We're making assumption that people from target group react on event X very different to others.</p>
<p>We have some sets of reaction numeric values on different type of events by those two groups... | https://math.stackexchange.com/questions/2971770/how-to-calculate-statistical-difference-of-two-samples-in-0-100-range |
Question: <p>The question is as follows:</p>
<p>Let X be a variable with bin(25,p)-distribution. We test <span class="math-container">$H_{0}$</span>: p <span class="math-container">$\geq$</span> 0.4 against <span class="math-container">$H_{1}$</span>: p < 0.4. If we want a power function of at least 0.6 in p = 0.3,... | https://math.stackexchange.com/questions/2983953/minimum-size-of-test-given-that-power-function-is-at-least-0-6-in-p-0-3 |
Question: <p>In a example about U-statistics, <span class="math-container">$h(x_1,x_2)=\frac 12(x_1-x_2)^2$</span>, then
<span class="math-container">$$U_n=\frac{2}{n(n-1)}\sum_{i<j}\frac{(X_i-X_j)^2}{2}=\frac{1}{n-1}\sum_{i=1}^{n}(X_i-\bar{X})^2$$</span>
I don't know how to prove it completely.</p>
Answer: <p>We k... | https://math.stackexchange.com/questions/3045070/how-to-prove-that-sum-ijx-i-x-j2-n-sum-i-1nx-i-barx2 |
Question: <p>We have an estimator <span class="math-container">$\hat{X}$</span> of <span class="math-container">$N$</span> which takes values in <span class="math-container">$\{1,2,\cdots,N\}$</span> with the following mass function:
<span class="math-container">$$P_N(\hat{X}=k) = \left(\frac{k}{N}\right)^n-\left(\frac... | https://math.stackexchange.com/questions/3072496/easy-hypothesis-testing-in-discrete-case-uniform-distribution |
Question: <p>in my wordbook it is said to be true, but I would like to know how to prove it. Let <span class="math-container">$X_1,X_2,...,X_n$</span> be distributed <span class="math-container">$Exp(\lambda)$</span> and <span class="math-container">$T(X_1,X_2,...,X_n)=X_1+X_2+...+X_n$</span> Prove that statistics T is... | https://math.stackexchange.com/questions/3085755/prove-that-statistics-is-sufficient |
Question: <p>They were talking about volcanoes today on TV, specifically the Popocatépetl and the threat of pyroclastic flows if a Plinian eruption happened. It was mentioned that because an eruption didn't occur in 1000 years (AD 800) there is an increasing probability.
Popular science, so intuitive, but what can be c... | https://math.stackexchange.com/questions/3168750/probability-on-a-time-basis |
Question: <p>If we think about a random variable following a discrete distribution then I can accept the association of a discrete value in data to the variable. For example, let's talk about n independent basketball shots each with probability p of making it into the hoop. The number of shots that make it in is distri... | https://math.stackexchange.com/questions/3174171/why-do-we-associate-discrete-values-to-data-from-a-continuous-distribution |
Question: <p>Here are two seperate question</p>
<p>Q1) An observed sample of four observations from a <span class="math-container">$N(u, \sigma^2)$</span> distribution has mean <span class="math-container">$62.75$</span> and standard deviation <span class="math-container">$4.57$</span>. Assess the hypothesis <span cla... | https://math.stackexchange.com/questions/3185558/when-to-use-t-test-or-z-test-when-computing-p-value |
Question: <p>My textbook mentioned this formula without any explanation: </p>
<p>s<sub>x</sub> = <span class="math-container">$\sqrt{\frac{{∑fm}^2}{n} − \bar{x}^2}$</span>
where
s<sub>x</sub> = sample standard deviation
<span class="math-container">$\bar{x}$</span> = sample mean</p>
<p>I thought the sample standard ... | https://math.stackexchange.com/questions/3214115/what-is-this-formula-for-sample-standard-deviation |
Question: <p>Let there be two random variables X and Y. A third random variable Z is defined as Z = X + Y. Suppose we are given <span class="math-container">$f_{XY}$</span> (the joint probability density function of X and Y).</p>
<p>How do we calculate <span class="math-container">$f_{ZY}$</span> (the joint probabilit... | https://math.stackexchange.com/questions/3216408/how-to-find-joint-pdf-of-z-and-y-where-z-x-y |
Question: <p>I have two deep learning classifiers and I want to make a test statistic to compare their performance against each other. The two algorithms have been tested on the same 60 samples and have an accuracy of 78.6% and 91.8% respectively. How do I compare their performance? Would I use Students paired t-test i... | https://math.stackexchange.com/questions/3272177/how-to-statistically-compare-the-outcome-of-two-classification-algorithms |
Question: <p>I'm trying to get a grasp on genetic inheritance laws. Assuming that chromosomes remain intact, would the 23rd row of Pascal's triangle accurately show the distribution of inheritance from a set of grandparents? The first number would be the occurrences of the 23 chromosomes split 0-23,then 1-22, 2-21 ..... | https://math.stackexchange.com/questions/3363570/pascals-triangle-and-inheritance-laws |
Question: <p>there are two samples, both with standard deviation 8.5.
If one combines the two samples together, find the relation between the standard deviation and 17.</p>
<p>I figure it cannot be determined. But I am not sure how to argue rigorously. Thank you!</p>
Answer: | https://math.stackexchange.com/questions/3424318/standard-deviation-of-two-samples |
Question: <p>I have a question on this specific question from the past entrance examination of a university.</p>
<p><a href="https://www.ism.ac.jp/senkou/kakomon/math_20190820.pdf" rel="nofollow noreferrer">https://www.ism.ac.jp/senkou/kakomon/math_20190820.pdf</a></p>
<p>I assume that the mean vector of the d-dimens... | https://math.stackexchange.com/questions/3459410/expected-value-of-xtax |
Question: <p>I've solved the following problem. </p>
<blockquote>
<p>An electronics firm receives, on the average, fifty orders per week for a particular silicon chip. If the company has sixty chips on hand, use the Central Limit Theorem to approximate the probability that they will be unable to fill all their order... | https://math.stackexchange.com/questions/3465210/when-do-you-have-to-apply-continuity-correction |
Question: <p>Suppose we are given a non-empty set of two or more points in <span class="math-container">$\mathbb{R}^2$</span>, <span class="math-container">$P$</span>, and we would like to quantify how <em>dense</em> those points are to one another. Let <span class="math-container">$\mathcal{D}(P)$</span> represent the... | https://math.stackexchange.com/questions/3510381/measuring-point-density-in-mathbbr2 |
Question: <p>How it s possible to calculate standard error for single sample, While standard error is defined as variance in different sample means?</p>
Answer: <p>The population has a (presumably unknown) variance. If you take a sample of size <span class="math-container">$n$</span> with replacement then the varianc... | https://math.stackexchange.com/questions/3552581/standard-error-and-standard-deviations |
Question: <p>If <span class="math-container">$X_1,X_2,…,X_n\sim Pois(λ)$</span>, find the UMVUE of <span class="math-container">$\exp(−2λ)$</span>.
I know based on lehmann scheffe theorem, the step is</p>
<p>(1)find <span class="math-container">$q(x)$</span> an unbiased estimater of <span class="math-container">$\exp(... | https://math.stackexchange.com/questions/3564547/what-is-the-umvue-of-exp-2-lambda-for-x-is-a-random-variable-with-poisson-d |
Question: <p>The batteries produced in a factory are tested before packing: 1.5% of batteries are found to be faulty, and are scrapped. Whether or not a battery is faulty is independent of each other. Experience suggested that a ‘good’ battery could last for 36 to 45 hours when used, and that all times within this rang... | https://math.stackexchange.com/questions/3609189/mean-and-standard-derivation-about-battery |
Question: <p>Two numbers are choosen at random from the sequence of number 1,2,3,.........n. what is the probability that one of them is less than k and other is greater than k?</p>
Answer: <p>If <span class="math-container">$k=1$</span> and <span class="math-container">$k=n$</span>, the probability is <span class="ma... | https://math.stackexchange.com/questions/3624952/k-being-given-probability-that-when-selecting-two-numbers-a-b-in-1-2-cd |
Question: <p><strong>Disclaimer</strong>: This problem is for my own understanding and not for a class in any way. </p>
<p>Greetings!</p>
<p>I am trying to solve the following problem but I am unsure how to proceed beyond what I have below. The trouble I am having is that $Z$ and $W$ and not independent of one anothe... | https://math.stackexchange.com/questions/2758870/ratio-of-certain-dependent-random-variables |
Question: <p>We have the following structure:</p>
<p>$\begin{bmatrix}
A & B & C & D\\
A & C & B & D\\
B & A & C & C\\
A & A & B & C
\end{bmatrix}$</p>
<p>It is required to tell which design is this CRD,LSD,RBD or factorial design?</p>
<p>I know it can't be LSD as it... | https://math.stackexchange.com/questions/2793969/identification-of-the-experimental-design |
Question: <p>Scenario: A company that makes cartons finds the probability of producing a carton with a puncture is 0.05. The probability that a carton has a smashed corner is 0.08. The probability that a carton has a puncture and a smashed corner is 0.004. </p>
<p>Question: If a quality inspector randomly selects a ca... | https://math.stackexchange.com/questions/2750166/probability-using-statistics |
Question: <p>Standard deviation is used as a measure of deviation or distribution in a sample or a population.Similarly mean is used as a measure of something in a group(say average marks of a group of students).How is standard deviation different from average deviation?</p>
Answer: <p>Let $(x_i)$ be a data set. Denot... | https://math.stackexchange.com/questions/2795144/how-is-standard-deviation-different-from-average-deviation |
Question: <p>It is known that probability density function (pdf) is not unique, but can we say the same about pmf?</p>
<p>Also, what can be the possible example where pdf or pmf may not exist?</p>
Answer: <p>If you want a simple example where it may not exist, consider the discrete uniform on -inf to inf. That is eac... | https://math.stackexchange.com/questions/2795856/is-probability-mass-function-pmf-unique |
Question: <p>An urn contains 3 red balls and 2 blue balls. A ball is drawn.
If the ball is red, it is kept out of the urn and a second ball is drawn from the urn.
If the ball is blue, then it is put back in the urn and a red ball is added to the urn.
Then a second ball is drawn from the urn.
(a) What is the probability... | https://math.stackexchange.com/questions/2776897/statistic-problem |
Question: <p>I have a question which I'm not sure how to phrase hence i couldn't find similar questions:</p>
<p>Usually all the examples i find online refer to dependent events and their probability of happening based on the event they depend on.</p>
<p>But in my question the issue is finding the probability of that ... | https://math.stackexchange.com/questions/2805564/probability-of-event-occurring-based-on-dependent-events |
Question: <p>I'm confused by the statement of the central limit theorem we've been given:</p>
<p>'If you take the sum $X$ of $N$ independent variables $x_i$, each taken from a distribution with mean $\mu_i$, then the distribution for $X$ has the average $\Sigma\mu_i$.'</p>
<p>So does this mean that if I take one numb... | https://math.stackexchange.com/questions/2762246/central-limit-theorem-independent-distributions |
Question: <p>For a project, I have to randomly choose exoplanets out of a database, but since the database has different sections, I have to choose one section. If one section has more exoplanets than another and I am randomly choosing five exoplanets, will the five exoplanets be more diverse if I choose the bigger or ... | https://math.stackexchange.com/questions/2797391/methodology-of-choosing-random-data |
Question: <p>What sample size is needed at the 95% confidence level, where the error (E) is 3 and the standard deviation is 20?</p>
<p>I can't figure out this question for the life of me and I am not sure of what formula to use. I know the answer is 171 but I would like to understand how we got there.</p>
Answer: <p>... | https://math.stackexchange.com/questions/2825564/what-sample-size-is-needed-at-the-95-confidence-level-where-the-error-e-is-3 |
Question: <p>Suppose X ∼ Poisson(λ), instead of estimating λ, we
are interesting in estimating P(X = 0)^2 = e^−2λ. Show that δ(X) = (−1)X is an unbiased estimator for e^−2λ
. Is this a good estimator? Why?</p>
<p>I'm having a bit of trouble starting this problem. I know that equation for Bias and all, but how do I use... | https://math.stackexchange.com/questions/1502767/unbiased-estimators-poisson |
Question: <p>Ok so this the question:</p>
<p>An administrator at a medium-sized hospital tells the board of directors that, among patients received at the Emergency room and eventually admitted to a ward, the average length of time between arriving at Emergency and being admitted to the ward is 4 hours and 15 minutes.... | https://math.stackexchange.com/questions/1272083/one-tailed-or-two-tailed |
Question: <p>Let's suppose we have two different processes, each generating some amount of money $M$ every second.</p>
<p>$$0 \leq M \leq 1000$$</p>
<p>We run each process for $50\%$ of available time.</p>
<p>The question is how to compare the productivity (in money; per second) of these two processes if there is n... | https://math.stackexchange.com/questions/1589763/compare-2-algorithms-by-statistics |
Question: <p>I have a simple algebra formula, proven to work. But I need help in understanding why it works.</p>
<p>The Scenario: I work at a call center, and am trying to calculate the time free in-between calls. I have the 3 variables, provided by Live data:</p>
<ul>
<li>Staff Available (not on calls)</li>
<li>Staf... | https://math.stackexchange.com/questions/1521759/please-explain-a-simple-formula-calculating-time-in-between-a-call-queue |
Question: <p>Let $X, Y$ have the joint pdf $f(x, y)= 2, \quad 0 < y < x < 1$</p>
<p>I'm trying to calculate the marginal probability density functions, but I don't know which intervals I'm supposed to use. The source I'm learning from will interchange the following</p>
<p>$f_X(x) = \int_0^x$</p>
<p>$f_Y(y) ... | https://math.stackexchange.com/questions/1571251/joint-probability-distributions-with-continuous-random-variables |
Question: <p>Hello I found a problem on statistics which make me a bit confused. Could anyone help? Thanks!</p>
<p>Let <em>X1</em>, <em>X2</em>, <em>X3</em> be independent random variables following exponential
distribution with parameter <em>θ</em>=$5$. What is the probability that the minimum of <em>X1</em>,
<em>X2<... | https://math.stackexchange.com/questions/1559403/what-is-the-probability-that-the-minimum-of-x1-x2-and-x3-is-larger-than-1 |
Question: <p>Suppose $X$ is a binomial random variable with parameters $(100, 1/3)$ and $Y$ is a geometric random variable with parameter 1/4.</p>
<p>(a) Find $E[(50 + X)^2]$.</p>
<p>(b) Find $Var(10 − 2Y )$.</p>
<p>a) I know that for a binomial random variable $E(X)=np$ and in this case $(n,p)=(100,1/3)$ so $E(X)=1... | https://math.stackexchange.com/questions/1560322/binomial-and-geometric-variables-finding-expected-values-and-variance |
Question: <p>$n=240$ trials with a $6$ sided dice</p>
<p>$X = \#5$'s</p>
<p>$Y = \#6$'s</p>
<p>How do I go about showing that $\operatorname{Cov}(X,Y) = -20/3$? I think I need to find $V(X+Y)$ but I'm not sure how. $V(X)=V(Y)=240* 1/6 * 5/6$. </p>
Answer: <p>That is the covariance if the die rolled 240 times is fai... | https://math.stackexchange.com/questions/1562631/how-can-i-find-operatornamecovx-y |
Question: <p>Let $\mu,\alpha_n:\mathbb R^+\to \mathbb R$ continuous function with $\mu$ bounded function.
Let $N^{(n)}$ the trajectory of a Poisson process with intensity $(\alpha_n \mu)(t)$.
Let $0=T_0^{(n)}<T_1^{(n)}<..$ jumps of $N^{(n)}$.</p>
<p>Let $M_n(t)=\sum_{i=1}^{N_t^{(n)}} \frac {1} {\alpha_n (T_i^{(n... | https://math.stackexchange.com/questions/1575235/unbiased-estimator-of-int-0t-mu-s-ds |
Question: <p><em>(Sorry for the inconvenience related to the tags, please feel free to correct my post if it needs a better scope by adding some other tags).</em></p>
<p><strong>CONTEXT</strong></p>
<p>I have several (decimal) numbers shaped like this :</p>
<ul>
<li>1.081</li>
<li>289.089167</li>
<li>2.98</li>
<li>.... | https://math.stackexchange.com/questions/1598451/get-precision-of-any-decimal-number |
Question: <p>If I know $\alpha=x_2-x_1$ and $\beta=(x_3-x_1)+(x_3-x_2)$, how can I calculate the variance of $\{x_1,x_2, x_3\}$?</p>
Answer: <p>$x_3-x_2=(x_3-x_1)-(x_2-x_1)$ allows you to easily obtain $x_k-x_1$. The shift by $x_1$ doesn't change the variance.</p>
| https://math.stackexchange.com/questions/1457954/how-can-i-calculate-the-variance-if-the-only-thing-i-know-is-the-difference-betw |
Question: <p>Let X have a normal distribution with mean μ and variance $\sigma^2$. Find $E[X^3]$ (in terms
of μ and $\sigma^2$).</p>
<p>Im pretty sure that $μ= E[X]$ so to find $E[X^3]$ would i just split it up into $E[X*X^2]$ since i know $E[X]$ and $E[X^2]$ can be found from the variance formula?</p>
Answer: <p><st... | https://math.stackexchange.com/questions/1564120/normal-distribution-finding-expectations |
Question: <p>I am trying to do the following problem
Suppose that $X_1,...,X_n\stackrel{iid}\sim N(0,1)$. Define $$\bar{X}_k=\frac{1}{k-1}\sum_{i=1}^{k-1}X_i,\,\,\,\,\,\,\text{for }k=2,3,.....,n
$$</p>
<p>(i) What is the joint distribution of $(X_2-\bar{X}_2,X_3-\bar{X}_3,...,X_n-\bar{X}_n)$?</p>
<p>(ii) What is the... | https://math.stackexchange.com/questions/1646896/finding-joint-distribution-for-the-following |
Question: <p>This <a href="https://math.stackexchange.com/q/1576971/290307">https://math.stackexchange.com/q/1576971/290307</a> question reminded me of a yet unanswered question I had as a student.</p>
<p><a href="https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test" rel="nofollow noreferrer">https://en.wikipedia... | https://math.stackexchange.com/questions/1577278/mann-whitney-utest-in-n-dimensions |
Question: <p>If $Y_1, Y_2, \ldots , Y_n$ denote a random sample from an exponential distribution with mean $θ$, then $E(Y_i)=θ$ and $V(Y_i)=θ^2$. Thus, $E(\bar Y)=θ$ and $V(\bar Y)=θ^2/n$, or $σ_Y=θ/\sqrt{n}$. Suggest an unbiased estimator for θ and provide an estimate for the standard error of your estimator.</p>
<p>... | https://math.stackexchange.com/questions/1647133/suggest-an-unbiased-estimator-for-%ce%b8-and-provide-an-estimate-for-the-standard-err |
Question: <p>I'm confused on how to find a function <span class="math-container">$g_{(1)}$</span> of the MLE that is a pivotal quantity. I've never seen such notation for a function before. Here is the problem statement:</p>
<p>Let <span class="math-container">$Y_1$</span>,<span class="math-container">$Y_2$</span>,...,... | https://math.stackexchange.com/questions/4989767/finding-a-function-that-is-a-pivotal-quantity-of-the-mle |
Question: <p>I just have a simple question on scaling a uniform distribution.
I know that uniform distribution has probability density of $1/(b-a)$ defined on the interval a to b. </p>
<p>My textbook says that we can scale the distribution to be between (0,1) and have a constant density of 1 by doing the following: <... | https://math.stackexchange.com/questions/314244/scaling-a-uniform-distribution-probability |
Question: <p>I have 3 random variables; X,Y, and Z. I am pretty familiar with law of total variance for two variables;</p>
<p><span class="math-container">$Var(X) = E[Var(X|Y)] + Var[E(X|Y)]$</span>.</p>
<p>(I'm sorry if the words are messy).</p>
<p>Recently, I read some papers, which state law of total variance using ... | https://math.stackexchange.com/questions/4185243/law-of-total-variance-using-three-different-variables |
Question: <p>For a set of column vectors $x_1,\dots,x_n$, the identity shows that $\sum_{i=1}^n x_i x_i^T = X^TX$. I can show this by seeing the $(p,q)$ entry of the resulting matrix is $\sum_{i=1}^n (X^T)_{pi}X_{iq} = \sum_{i=1}^n x_{ip} x_{iq}$. Is there a quicker way of seeing this? and, does $xx^T$ have a special n... | https://math.stackexchange.com/questions/210920/a-question-about-sum-i-1n-x-i-x-it-xtx |
Question: <p>Various statistical techniques are based on the assumption that two samples have the same variance and Bartlett's test is meant to check for that. Using R I made a few tests with randomly generated numbers. For example:</p>
<p>bartlett.test(list(rnorm(10,sd=1),rnorm(10,sd=2)))</p>
<p>will perform a Bartl... | https://math.stackexchange.com/questions/1136378/type-ii-errors-in-bartletts-test |
Question: <p>I've recently been going through Khan Academy Statistics, and I recently came across the fact that sample standard deviation is biased. Now, I know that there are many proofs online including several on math stack exchange, but I was wondering if someone could give me some intuition for why this happens in... | https://math.stackexchange.com/questions/3145907/why-is-sample-standard-deviation-biased |
Question: <p>I have seen <a href="https://math.stackexchange.com/questions/3622994/random-sample-random-variables-or-realizations-of-the-same-random-variable">this</a> question and it does not quite answer my question.</p>
<p>I have always had some confusion about the concept of a random variable, and how in statistics... | https://math.stackexchange.com/questions/5038130/sample-random-variable-or-both |
Question: <p>How can I calculate the mode in a grouped frequency distribution when the largest frequency occurs in two or more classes?</p>
Answer: <p>If the you have a frequency distribution where the largest frequency occurs in two or more classes, then we call it a <a href="https://en.wikipedia.org/wiki/Multimoda... | https://math.stackexchange.com/questions/1311506/calculating-mode-in-a-grouped-frequency-distribution |
Question: <p><span class="math-container">$T_1$</span> and <span class="math-container">$T_2$</span> are unbiased estimators of <span class="math-container">$\theta$</span>.
Then <span class="math-container">$T_3=aT_1+(1-a)T_2$</span> is also an unbiased estimator of <span class="math-container">$\theta$</span>.</p>
<p... | https://math.stackexchange.com/questions/1902968/variance-of-an-unbiased-estimator |
Question: <p>It is often said that degree of freedom causes the need for standard deviation formula to be corrected. When explaining degree of freedom, it is often said that when one knows the mean of the formula, only $n-1$ data are actually needed, as the last data can be determined using mean and $n-1$ data. However... | https://math.stackexchange.com/questions/487954/degree-of-freedom-and-corrected-standard-deviation |
Question: <p>Apologies for the format of this question - I am new to this website. I am having trouble with part (c) of the question below, if anyone could assist that would be great.</p>
<p>Thanks in advance</p>
<p>Suppose that two independent random samples of size $n_1$ and $n_2$ observations are selected from nor... | https://math.stackexchange.com/questions/803199/pooled-variance-estimator-efficiency |
Question: <p>I am comparing the drug exposures across two different groups, consisting of 1000 simulated drug exposures per group. Drug exposures are continuous variables following a normal distribution.</p>
<p>I want to know if different doses yield a statistically significant difference in mean drug exposure across t... | https://math.stackexchange.com/questions/3732609/statistical-comparisons-for-large-sample-sizes-n-1000 |
Question: <p>Two players, who have equal chances of winning each round, compete for a money prize. The first player to
win three rounds collects the total amount.
(a) If the game is interrupted when the score was 2 to 1, how should the players divide the stakes fairly?
(b) What if the game was interrupted when the scor... | https://math.stackexchange.com/questions/4446346/statistics-how-to-solve-this-problem |
Question: <p>I am reading a book, it said:</p>
<blockquote>
<p>The expected power of a Monte Carlo test can be quite good even for
relatively small values of m. In simple situations (testing means, for
example), m = 99 may be a good choice. This allows the p-value to be
expressed simply in two decimal places. In more c... | https://math.stackexchange.com/questions/4448901/ask-a-question-of-monte-carlo-test |
Question: <p>Find <span class="math-container">$c$</span> for <span class="math-container">$P(\frac{5}{12}-c \le Y \le \frac{5}{12}+c)=\frac{1}{2}$</span></p>
<p>We also have that
<span class="math-container">$$f_Y(y) = k\sum_{i=0}^{\infty}y^i, y\in(1/3, 1/2) \\ \implies k\int_{1/3}^{1/2}\frac{1}{1-y}dy \implies k=\fra... | https://math.stackexchange.com/questions/4449026/find-c-for-p-frac512-c-le-y-le-frac512c-frac12 |
Question: <p>1) In a population of men, the probability that a man’s left eye is of brown colour is p, and the probability that a man’s right eye colour is brown is also p. Therefore the probability that a man has at least one eye of brown colour is:
Pr(left eye brown or right eye brown)
= Pr(left eye brown) + P(rig... | https://math.stackexchange.com/questions/1930501/whats-wrong-with-this-approaches |
Question: <p>I've had a look for intuitive explanations of the variance of an RV (e.g. <a href="https://math.stackexchange.com/questions/5392/intuitive-explanation-of-variance-and-moment-in-probability">Intuitive explanation of variance and moment in Probability</a>) but unfortunately for me, I still don't feel comfort... | https://math.stackexchange.com/questions/31126/usefulness-of-variance |
Question: <p>I am trying to establish correlation between tossing of coins and occurring of repeats.</p>
<blockquote>
<p>Coin is flipped 10 time as follows:</p>
<p><span class="math-container">$${\rm H.T.H.H.H.T.H.T.T.T. }$$</span></p>
<p>After each repeat occurring I have put (R) as follows:</p>
<p><span class="math-c... | https://math.stackexchange.com/questions/128892/relation-between-repeat-number-in-coin-toss |
Question: <p>I'm doing some revision here and I think one of the answers in my notes is wrong. It says on my notes the answer is D). Here's the question:</p>
<blockquote>
<p>A researcher conducted a large sample two-sided test of the null hypothesis that <span class="math-container">$u = 100$</span>. She reports a <spa... | https://math.stackexchange.com/questions/139553/question-on-p-value-for-two-sided-test |
Question: <blockquote>
<p>I find the mass of liquid in a container by using</p>
<blockquote>
<p>mass of liquid = mass of (container+liquid) - mass of container</p>
</blockquote>
<p>My measurements are subject to an error with mean zero and standard deviation 0.7g. Find the standard deviation of the error in the calcula... | https://math.stackexchange.com/questions/285101/combining-errors-given-standard-deviation |
Question: <blockquote>
<p>Let X and Y be discrete random variable with joint pdf <span class="math-container">$f(x,y) = 4/5xy$</span> if <span class="math-container">$x = 1,2$</span> and <span class="math-container">$y = 2,3$</span> and zero otherwise. Find:</p>
<p>E(Y)</p>
</blockquote>
<p>Basically I found the margin... | https://math.stackexchange.com/questions/232669/expected-value-calculation |
Question: <p>Currently, I am studying statistics as an undergraduate. Our lecture today finished with information about obtaining probability distributions and expected values (using binomial and geometric distributions).</p>
<p>Later that day, after throwing some snow with some friends, I figured it would be neat to u... | https://math.stackexchange.com/questions/1628596/how-to-obtain-this-particular-probability-distribution-and-standard-deviation |
Question: <blockquote>
<p>The city needs to perform some road maintenance and will rent excavator machines from a company. Each excavator will work for at least one hour and no more than <span class="math-container">$4$</span> hours in a day. The working time is evenly distributed.</p>
<p>Given that a excavator has... | https://math.stackexchange.com/questions/1712484/uniform-distribution-for-probability |
Question: <p>It's a very basic high school statistical question, but I'm struggling to solve it.</p>
<p>Suppose I have a school with <span class="math-container">$287$</span> students and each one made a test with <span class="math-container">$50$</span> questions (multiple choice questions with <span class="math-conta... | https://math.stackexchange.com/questions/2332766/which-subject-are-these-students-best-basic-high-school-statistical-question |
Question: <p>The short form of my question is :</p>
<p>Test A shows a useful result after one trial at 16% chance, two trials at 41,7% chance and after three trials with 75% chance. Is it better or worse to use it compared to test B which needs at least two trials and shows a useful result after two trials at 33,3% cha... | https://math.stackexchange.com/questions/3728841/how-to-evaluate-which-test-method-is-better |
Question: <p>We have 81.000 different marbles in a box. With every grab, I get 30 different marbles out of the box. After this, the 30 marbles have to be thrown back into the box so that there are again 81.000 different marbles.</p>
<p>How often do I have to grab into the box until I have statistically seen at least on... | https://math.stackexchange.com/questions/3739900/amount-of-trials-until-all-marbles-have-shown-in-a-box-of-different-marbles |
Question: <p>I have sets of elements (lets call each <code>S</code>). The elements in each <code>S</code> can only ever be <code>black</code> or <code>white</code>. I also have a test that determines if an element is <code>black</code> or <code>white</code>, with some false-positive/false-negative rate <code>FP</code>/... | https://math.stackexchange.com/questions/4725391/how-to-choose-size-of-samples-to-determine-if-set-contains-elements |
Question: <p>Lets say that we are trying to find the variance of a coin with a <span class="math-container">$0.6$</span> probability of heads flipped <span class="math-container">$n$</span> times.
(Binomial with <span class="math-container">$p=0.6$</span>)</p>
<p>Given that the equation to find variance is <span class... | https://math.stackexchange.com/questions/3202867/how-to-calculate-ex2-in-order-to-find-variance |
Question: <p>The rule:</p>
<p>In statistics, the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within 3 standard deviations of the mean in a normal distribution.</p>
<p>About 68.27% of the values lie within 1 standard deviation of the mean. Similarly, about 9... | https://math.stackexchange.com/questions/493046/precise-mathematical-translation-of-the-68-95-99-7-rulenot-a-proof |
Question: <p>I have two sets of products A + B in the same product category. I have the overall and A's N, mean and variance. Can I calculate the variance of B with this?</p>
<p>I noticed <a href="https://stats.stackexchange.com/questions/29170/how-to-compute-standard-deviation-of-difference-between-two-data-sets">thi... | https://math.stackexchange.com/questions/2238086/calculate-variance-of-a-subset |
Question: <p>I have a shape <span class="math-container">$S$</span> of area <span class="math-container">$A$</span>, but I do not know what <span class="math-container">$A$</span> is. However, I do have the coordinates of <span class="math-container">$N$</span> points (the coords are <span class="math-container">$(x_i,... | https://math.stackexchange.com/questions/4732599/estimation-of-shape-area-given-random-points-inside-it |
Question: <blockquote>
<p>If the mean of a set of data is equal to the mode, is it always equal to the median? Explain why or why not.</p>
</blockquote>
<p>I would guess no, but after generating countless sets I cannot find anything that contradicts this</p>
Answer: | https://math.stackexchange.com/questions/2227286/if-mean-mode-mean-median |
Question: <p>This was found in a line from the proof of the law of large numbers. the $1\{X>C\}$ is the usual indicator function. </p>
Answer: <p>Define $Y = I\{X>c\}$ then
$$
EI\{X>c\} =EY = 1P(X>c)+0P(X\le c) = P(X>c).
$$
You can see that $Y \sim Bernoulli ( P(X>c))$.</p>
| https://math.stackexchange.com/questions/2244758/why-is-pxc-e1-xc |
Question: <p>I like to ask you about salary payment scheme by a company. Here is interesting points of this company salary scheme. </p>
<p><strong>New company payroll scheme</strong></p>
<ol>
<li>Salary is credit on every 25th of every month. </li>
<li>Number of working days is 30 days flat. </li>
<li>A few people ar... | https://math.stackexchange.com/questions/2227472/salary-scheme-is-hr-is-cheating |
Question: <p>an urn contains 25 balls 40% of which are green. a contestant reaches in the urn to choose three balls the contestant will win 200 if he or she selects a green ball but will lose 120 for any other colour. is this a fair game</p>
<p>A) the ball is replaced after each draw
B) the ball is not replaced after ... | https://math.stackexchange.com/questions/2165837/fair-game-question |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.