# Question: Find the mean and the variance of the sampling distribution

Find the mean and the variance of the sampling distribution of Y1 for random samples of size n from the population of Exercise 8.46.

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Find the sampling distributions of Y1 and Yn for random samples of size n from a population having the beta distribution with α = 3 and β = 2. With reference to part (b) of Exercise 8.52, find the covariance of Y1 and Yn. Looking at binomial random variables as on page 226, that is, as sums of identically distributed independent Bernoulli random variables, and using the central limit theorem, prove Theorem 6.8 on page 191. Rework part (b) of Exercise 8.66, assuming that the population is not infinite but finite and of size N = 400. The claim that the variance of a normal population is σ2 = 25 is to be rejected if the variance of a random sample of size 16 exceeds 54.668 or is less than 12.102. What is the probability that this claim will be rejected ...Post your question