Show that if we let θ = M/N in Theorem 5.7, the mean and the variance of the hypergeometric distribution can be written as µ = nθ and σ2 = nθ(1– θ) ∙ N – n / N – 1 . How do these results tie in with the discussion on page 156?
Answer to relevant QuestionsWhen calculating all the values of a Poisson distribution, the work can often be simplified by first calculating p(0;λ) and then using the recursion formula Verify this formula and use it and e–2 = 0.1353 to verify the ...Derive the formulas for the mean and the variance of the Poisson distribution by first evaluating E(X) and E[ X(X – 1)]. An automobile safety engineer claims that 1 in 10 automobile accidents is due to driver fatigue. Using the formula for the binomial distribution and rounding to four decimals, what is the probability that at least 3 of 5 ...Verify that (a) b(x; n,θ) = b(n - x; n, 1 - θ). Also show that if B(x; n,θ) For x = 0,1,2,…,n, then (b) b(x; n,θ) = B(x; n,θ)- B(x- 1; n,θ); (c) b(x; n,θ) = B(n- x; n, 1-θ)- B(n- x- 1; n,1- θ); (d) B(x; n,θ) ...An alternative proof of Theorem 5.2 may be based on the fact that if X1, X2, . . ., and Xn are independent random variables having the same Bernoulli distribution with the parameter ., then Y = X1 + X2 + · · · + Xn is a ...
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