Question: If X has a hypergeometric distribution with M 3
If X has a hypergeometric distribution with M = 3, N = 6, and n = 2, find the probability distribution of Y, the number of successes minus the number of failures.
Answer to relevant QuestionsUse 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 ...Find the mean and the variance of the finite population that consists of the 10 numbers 15, 13, 18, 10, 6, 21, 7, 11, 20, and 9. Verify the identity Which we used in the proof of Theorem 8.11. With reference to Exercise 8.2, show that if the two samples come from normal populations, then 1 – 2 is a random variable having a normal distribution with the mean µ1 – µ2 and the variance σ21/n1 + σ22/n2. 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.
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