# Question: Use the corollary of Theorem 4 15 on page 136 to

Use the corollary of Theorem 4.15 on page 136 to show that if X1, X2, . . . , Xn constitute a random sample from an infinite population, then cov(Xr – , ) = 0 for r = 1, 2, . . . , n.

Theorem 4.15

If the random variables X1, X2, . . . , Xn are independent and

Then

Theorem 4.15

If the random variables X1, X2, . . . , Xn are independent and

Then

**View Solution:**## Answer to relevant Questions

Use the condition of Exercise 8.9 to show that the central limit theorem holds for the sequence of random variables of Exercise 8.8. In exercise Show that the variance of the finite population {c1, c2, . . . , cN} can be written as Also, use this formula to recalculate the variance of the finite population of Exercise 8.16. Use Theorem 8.11 to show that, for random samples of size n from a normal population with the variance σ2, the sampling distribution of S2 has the mean σ2 and the variance 2σ4/n–1. (A general formula for the variance of ...Use Stirling’s formula of Exercise 1.6 on page 16 to show that when v → ∞, the t distribution approaches the standard normal distribution. Show that the F distribution with 4 and 4 degrees of freedom is given by And use this density to find the probability that for independent random samples of size n = 5 from normal populations with the same variance, S21 / ...Post your question