# Question: Explain why when we sample with replacement from a finite

Explain why, when we sample with replacement from a finite population, the results of Theorem 8.1 apply rather than those of Theorem 8.6.

## Relevant Questions

Explain the results of Exercise 5.28 on page 164 in light of Theorem 8.6. Show that the formula for the sample variance can be written as Also, use this formula to recalculate the variance of the sample data of Exercise 8.18. Based on the result of Exercise 8.24, show that if X is a random variable having a chi– square distribution with v degrees of freedom and v is large, the distribution of X – v / √2v can be approximated with the ...Show that for v2 > 2 the mean of the F distribution is v2 / v2 – 2, making use of the definition of F in Theorem 8.14 and the fact that for a random variable V having the chi-square distribution with v2 degrees of freedom, ...Find the sampling distributions of Y1 and Yn for random samples of size n from a continuous uniform population with α = 0 and β = 1.Post your question