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, E(1/V) = 1/v2 – 2.
Answer to relevant QuestionsVerify that if X has an F distribution with v1 and v2 degrees of freedom and v2 → ∞, the distribution of Y = v1X approaches the chi-square distribution with .1 degrees of freedom. 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. If the first n1 random variables of Exercise 8.2 have Bernoulli distributions with the parameter θ1 and the other n2 random variables have Bernoulli distributions with the parameter θ2, show that, in the notation of ...Use the result of Exercise 8.56 to find the mean and the variance of the sampling distribution of R for random samples of size n from the continuous uniform population of Exercise 8.46. A random sample of size n = 100 is taken from an infinite population with the mean µ = 75 and the variance σ2 = 256. (a) Based on Chebyshev’s theorem, with what probability can we assert that the value we obtain for X ...
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