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.
Answer to relevant QuestionsUse Theorem 4.14 on page 135 and its corollary to show that if X11, X12, . . . , X1n1 , X21, X22, . . . , X2n2 are independent random variables, with the first n1 constituting a random sample from an infinite population with ...Show that if X1, X2, . . . , Xn are independent random variables having the chi-square distribution with v = 1 and Yn = X1 + X2 + · · · + Xn, then the limiting distribution of As n → ∞ is the standard normal ...Use Stirling’s formula of Exercise 1.6 on page 16 to show that when v → ∞, the t distribution approaches the standard normal distribution. Verify that if Y has a beta distribution with α = v1/2 and β = v2/2 , then X = v2Y/v1(1 – Y) Has an F distribution with v1 and v2 degrees of freedom. Find the sampling distribution of Y1 for random samples of size n = 2 taken (a) Without replacement from the finite population that consists of the first five positive integers; (b) With replacement from the same ...
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