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In: Statistics and Probability

Using I.uniform,II binomial , III. exponential and IV. Poisson random variable for each solve the following...


Using I.uniform,II binomial , III. exponential and IV. Poisson random variable for each solve the following


A.
What is the average of the 500 sample means when the sample size is n = 5? What is the average of the 500 sample means when the sample size is n = 50? What are the theoretical expected values of sample means, respectively?
b. For n = 5 and n = 50, what are the variances of the 500 sample means, respectively? What are the theoretical variances of sample means, respectively?



C. After answering parts a-d for all distributions I-IV, you should see some common trends across distributions. Summarize these findings for each of a-c and use the central limit theorem to explain your findings.

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