Great traverse for smaller loads. We have it "hochkant" as a carrier for small (thus also quite light) LED spotlights in use two pieces connected by conical connectors hold really very firm .Pass accuracy and Roadtauglichkeit are outstanding as well as the entire processing. As said for Smaller loads.
M&S Blackheath Simply Food offers our renowned range of food, drink and fresh produce, which mixes innovation, great value and delicious flavours. Whether it's healthy-cooking inspiration, mouth-watering prepared foods, or event-ready celebration bites and platters, you're sure to find something to delight.
This year we are celebrating 120 years of serving Radstock. We are a traditional hardware shop, and what we do hasn't really changed very much since the shop first opened in 1898, selling housewares and ironmongery. Mr Orchard was the owner at that time. The shop was later transferred to Mr Tiley, who ran it for many years. He had a fleet of delivery vehicles, taking housewares and paraffin to the people of Radstock. In 1973 Mr Thomson took over. He is now well into his 90's, but the business is run by daughter, Jo Milling with the help of Steve, Evan Paula, Adam, and Mr Thomson's grandson Alistair.
You may be surprised to learn that much of your life consists of constructing arguments. If you ever plead a case to your parents—in order to extend your curfew, or to get a new gadget, for example—you are using persuasive strategies.
When you discuss music with friends and agree or disagree with them about the merits of one singer compared to another, you are also using strategies for persuasion.
Here's a surprise: when you engage in these "arguments" with your parents and friends, you are instinctively using ancient strategies for persuasion that were identified by the Greek philosopher Aristotle a few thousand years ago!
When you write a research paper, write a speech, or participate in a debate, you also use the persuasion strategies mentioned above. You come up with an idea (a thesis) and then construct an argument to convince readers that your idea is sound.
You should become familiar with pathos, logos, and ethos for two reasons. First, you need to develop your own skills at crafting a good argument, so that others will take you seriously.
Secondly, you must develop the ability to identify a really weak argument, stance, claim, or position when you see or hear it.
Logos refers to an appeal to reason based on logic. Logical conclusions come from assumptions and decisions derived from weighing a collection of solid facts and statistics. Academic arguments (research papers) rely on logos.
An example of an argument that relies on logos is the argument that smoking is harmful based on the evidence that "Cigarette smoke contains over 4,800 chemicals, 69 of which are known to cause cancer." (1)
As a researcher, your job is to find statistics and other facts to back up your claims. When you do this, you are appealing to your audience with logic or logos.
Trustworthiness is important in research, as you well know. You must trust your sources, and your readers must trust you.
In the example above concerning logos, you saw two examples that were based on hard facts (numbers). However, one example comes from the American Lung Association. The other comes from Facebook fan pages. Which of these sources do you suppose is more credible?
Facebook fan pages can be started by anyone. Lady Gaga may have fifty different fan pages, and each page may contain duplicate "fans." The fan page argument is probably not very sound (even though it seems logical).
The facts provided by the American Lung Association are probably more persuasive than those provided by fan pages since the American Lung Association has been around for more than 100 years.
At first glance, you might think that your own credibility is out of your control when it comes to posing academic arguments but that is wrong!
Even if you write an academic paper on a topic that is outside your area of expertise, you can improve your credibility (persuade through ethos) as a researcher by coming across as a professional--by citing credible sources and making your writing error-free and concise.
Pathos refers to appealing to a person by influencing their emotions. Pathos is involved in the strategy of convincing the audience by invoking feelings through their own imaginations.
You probably appeal through pathos when you try to convince your parents of something. Consider this statement:
While that statement is true, the real power lies in the emotions that you will likely invoke in your parent. What mother wouldn't envision a broken-down automobile perched by the side of a busy highway upon hearing that statement?
There may or may not be a place for pathos in your research paper. For example, you may be writing an argument essay about the death penalty.
Ideally, your paper should contain a logical argument. You should appeal to logos by including statics to support your view such as data that suggests that the death penalty does/does not cut down on crime (there's plenty of research both ways).
But you may also use pathos by interviewing someone who witnessed an execution (on the anti-death penalty side) or someone who found closure when a criminal was executed (on the pro-death penalty side).
Generally, however, academic papers should employ appeals to emotions pretty sparingly. A long paper that is purely based on emotions is not considered very professional!
Even when you are writing about an emotionally-charged, controversial issue like the death penalty, you can't write a paper that is all emotion and opinion. The teacher, in that circumstance, will likely assign a failing grade because you haven't provided a sound (logical) argument.
1. From the website for The American Lung Association, "General Smoking Facts," accessed on December 20, 2011.
Suppose that we have a random sample from a population of interest. We may have a theoretical model for the way that the population is distributed. However, there may be several population parameters of which we do not know the values. Maximum likelihood estimation is one way to determine these unknown parameters.
The basic idea behind maximum likelihood estimation is that we determine the values of these unknown parameters. We do this in such a way to maximize an associated joint probability density function or probability mass function. We will see this in more detail in what follows. Then we will calculate some examples of maximum likelihood estimation.
Start with a sample of independent random variables X1, X2, . . . Xn from a common distribution each with probability density function f(x;θ1, . . .θk). The thetas are unknown parameters.
Since our sample is independent, the probability of obtaining the specific sample that we observe is found by multiplying our probabilities together. This gives us a likelihood function L(θ1, . . .θk) = f( x1 ;θ1, . . .θk) f( x2 ;θ1, . . .θk) . . . f( xn ;θ1, . . .θk) = Π f( xi ;θ1, . . .θk).
More specifically, we differentiate the likelihood function L with respect to θ if there is a single parameter. If there are multiple parameters we calculate partial derivatives of L with respect to each of the theta parameters.
To continue the process of maximization, set the derivative of L (or partial derivatives) equal to zero and solve for theta.
We can then use other techniques (such as a second derivative test) to verify that we have found a maximum for our likelihood function.
Suppose we have a package of seeds, each of which has a constant probability p of success of germination. We plant n of these and count the number of those that sprout. Assume that each seed sprouts independently of the others. ow do we determine the maximum likelihood estimator of the parameter p?
We begin by noting that each seed is modeled by a Bernoulli distribution with a success of p. We let X be either 0 or 1, and the probability mass function for a single seed is f( x ; p ) = px (1 - p)1 - x.
Our sample consists of n different Xi, each of with has a Bernoulli distribution. The seeds that sprout have Xi = 1 and the seeds that fail to sprout have Xi = 0.
Next we differentiate this function with respect to p. We assume that the values for all of the Xi are known, and hence are constant. To differentiate the likelihood function we need to use the product rule along with the power rule:
Now, in order to continue the process of maximization, we set this derivative equal to zero and solve for p:
Thus Σ xi = p n and (1/n)Σ xi = p. This means that the maximum likelihood estimator of p is a sample mean. More specifically this is the sample proportion of the seeds that germinated. This is perfectly in line with what intuition would tell us. In order to determine the proportion of seeds that will germinate, first consider a sample from the population of interest.
There are some modifications to the above list of steps. For example, it as we have seen above, is typically worthwhile to spend some time using some algebra to simplify the expression of the likelihood function. The reason for this is to make the differentiation easier to carry out.
Another change to the above list of steps is to consider natural logarithms. The maximum for the function L will occur at the same point as it will for the natural logarithm of L. Thus maximizing ln L is equivalent to maximizing the function L.
Many times, due to the presence of exponential functions in L, taking the natural logarithm of L will greatly simplify some of our work.
We see how to use the natural logarithm by revisiting the example from above. We begin with the likelihood function:
The use of the natural logarithm of L(p) is helpful in another way. It is much easier to calculate a second derivative of R(p) to verify that we truly do have a maximum at the point (1/n)Σ xi = p.
For another example, suppose that we have a random sample X1, X2, . . . Xn from a population that we are modelling with an exponential distribution. The probability density function for one random variable is of the form f( x ) = θ-1 e -x/θ
The likelihood function is given by the joint probability density function. This is a product of several of these density functions:
Once again it is helpful to consider the natural logarithm of the likelihood function. Differentiating this will require less work than differentiating the likelihood function:
We see from this that the sample mean is what maximizes the likelihood function. The parameter θ to fit our model should simply be the mean of all of our observations.
There are other types of estimators. One alternate type of estimation is called an unbiased estimator. For this type, we must calculate the expected value of our statistic and determine if it matches a corresponding parameter.