[DOC] [TLE] The Binomial Distribution [PAR] In this section we will study the random variable that gives the number of ... The 
underlying distribution, the binomial distribution, is one of the most ... In almost all 
cases, note that the proof from Bernoulli trials is the simplest and most elegant. 
..... Thus, the density function at first increases and then decreases, reaching its... [DOC] [TLE] The Central Limit Theorem [PAR] the binomial distribution in the setting of Bernoulli trials; the negative ..... More 
generally, we can use the stationary and independence properties to find the ..... 
This is the version that we will give and prove, but first we need a generalization 
of a ..... hence we are approximating a discrete distribution with a continuous one. [DOC] [TLE] Bernoulli trials An experiment, or trial, whose outcome can be ... [PAR] A random variable is called a Binomial(n,p) random variable if it has the pmf, ... 
Can also be proved using mgf's: ... What is the probability that there will be no 
more than two ... Only one customer can arrive during each time interval. ..... X is 
an exponential random variable with parameters  (>0) if the pdf of X is given by. 
<. =. [DOC] [TLE] Continuous distributions, and their relation to discrete ones [PAR] chapters extend to the continuous case, thanks to its nature as a limit. Thus, .... 
This is the survival function of an exponential distribution, as can be seen 
immediately. ... De Moivre proved by brute calculation that a sequence of 
binomial distributions with ... , a constant (this is the verbal statement of the Law 
of Large. [DOC] [TLE] Power Series - UC Davis Mathematics [PAR] we can use them to define transcendental functions such as the exponential ... 
First, we prove that every power series has a radius of convergence. ... There is 
an 0  R   such that the series converges absolutely ... the power series 
converges as its interval of convergence, which is one of ..... From the binomial 
theorem,. [DOC] [TLE] Central Limit Theorem - Dartmouth College [PAR] that Sn has as its distribution the binomial probabilities b(n, p, j). In Section ... 
pected value np, which causes their spike graphs to drift off to the right as n in- ... 
the sum of the heights of the spikes equals one, the area under this curve would 
be ... The proof of this theorem can be carried out using Stirling's approximation 
from. [DOC] [TLE] exponential function - Compound interest derivation of $e ... [PAR] Feb 16, 2013 ... exponential-function ... There is more than one way to prove this statement. What 
exactly are .... Now I will show that its limit is exactly e . Let l be... [DOC] [TLE] Lecture Notes: Complex Numbers and the Complex Exponential [PAR] be very useful to assume that there is a number i for which one has ... Since any 
complex number is specified by two real numbers one can visualize them ... 22 
+ 12 = 5. z lies in the first quadrant so its argument  is an angle between 0 ...... 
(6) To prove or disprove the statements set z = a + bi, w = c + di and substitute in
... [DOC] [TLE] Week 4  Complex Numbers - Mathematical Institute [PAR] other numbers then the two roots of the quadratic can be written in the form ... 
complex numbers by adding their real and imaginary parts:- .... Note that the 
conjugate z of a point z is its mirror image in the real axis. ... A selection of the 
above statements is proved here; the remaining ones are left ...... by the binomial 
theorem. [DOC] [TLE] Notes on the Matrix Exponential [PAR] If a matrix A is diagonalizable, then there exists an invertible P so that A = PDP1, 
... It now follows from () and the binomial theorem that ... Both the statement of 
this theorem and the method of its proof will be important for the study of 
differential ..... If one is given a different initial value of Y , say Y (t0) at time t0, 
then the... [DOC] [TLE]

Question: It's a statement that can be proved; there are binomial & exponential ones
Answer: theorem