Question

a) What is a sampling distribution (include an APA citation)? _________

b) What is the Law of Large Numbers?________

3) Describe in your own words (do not directly quote any source) the difference between the distribution of a sample and the sampling distribution. Use an example in which the original population has a binomial distribution. You will probably use concepts from the book or another source, so be sure to cite any concepts that come from such sources (even if you paraphrase).

Answer 1

The distribution of statistic ( sample mean, sample range, sample variance, and so on) is called as sampling distribution.

b ) Tthe study the converges of the sequence in probability of a random varable for large sample size is called as th law of Large Numbers.

3) The distribution of sample means the relative frequencies of each value of the sample of the relative frequencies of the classes.

Sampling distribution is theoretical distribution can be obtained by transformation of the random variable.

Consider the example of Binomial distribution with parameter n = 5, and p = 0.5

Suppose we take a sample of size 10 from the above binomial distribution and we get the following sample

Then the distribution of these sample is as follows

.

The sampling distribution of sum of the binomial variables of equal probability of success ( p) is also binomial with parameters (n₁ + n₂ + ...+ n_k ) and p .

Where n₁, n₂, ....., n_k are the number of trials of each binomial variables.