Verify that if T has a t distribution with v degrees of freedom, then X = T2 has an F distribution with v1 = 1 and v2 = v degrees of freedom.
Answer to relevant QuestionsIf X has an F distribution with v1 and v2 degrees of freedom, show that Y = 1/X has an F distribution with v2 and v1 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. Duplicate the method used in the proof of Theorem 8.16 to show that the joint density of Y1 and Yn is given by (a) Use this result to find the joint density of Y1 and Yn for random samples of size n from an exponential ...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. The following is a sufficient condition for the central limit theorem: If the random variables X1, X2, . . . , Xn are independent and uniformly bounded (that is, there exists a positive constant k such that the probability ...
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