If X is a hypergeometric rv, show directly from the definition that E(X) = nM/N ( consider only the case n < M). [Hint: Factor nM/N out of the sum for E(X), and show that the terms inside the sum are of the form h( y; n – 1, M – 1, N -1), where y – x -1.]

Answer : Step 1 : Given If X is a hypergeometric rv. Now we have to show that directly from the definition that E(X) = N Here X:hypergeometric row variable. P(X = x)=h(x;n,m,N) Proposition : If X is the number of S’s in a completely random sample of size n drawn from a population consisting of M S’s and (N-M) F’s , then the probability distribution of X, called the hypergeometric distribution, is given by M NM (x)( nx ) P(X = x) = h(x; n, M, N) = N (n) X= the number of successes from a sample size of n, from a population of size N, with...