When calculating all the values of a hypergeometric distribution, the work can often be simplified by first calculating h(0; n, N, M) and then using the recursion formula
Verify this formula and use it to calculate the values of the hypergeometric distribution with n = 4, N = 9, and M = 5.
Answer to relevant QuestionsVerify the expression given for E[X(X – 1)] in the proof of Theorem 5.7. Suppose that f(x, t) is the probability of getting x successes during a time interval of length t when (i) The probability of a success during a very small time interval from t to t + △t is α ∙ △t, (ii) The ...If X1, X2, . . . , Xk have the multinomial distribution of Definition 5.8, show that the covariance of Xi and Xj is –nθiθj for i = 1, 2, . . . , k, j = 1, 2, . . . , k, and i ≠ j. Definition 5.8 The random variables ...With reference to Exercise 5.44, suppose that the percentage had been 51 instead of 50. Use a suitable table or a computer printout of the binomial distribution with n = 18 and θ = 0.51 to rework the three parts of that ...If the probability is 0.75 that a person will believe a rumor about the transgressions of a certain politician, find the probabilities that (a) The eighth person to hear the rumor will be the fifth to believe it; (b) The ...
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