Question: This exercise extends the hypergeometric distribution to multiple variables. Consider a population with N items of k different types. Assume that there are N 1

This exercise extends the hypergeometric to multiple variables. Consider a population with N items of k different types. Assume that there are N₁items of type 1, N₂items of type 2,€¦, N_kitems of type k so that N₁+ N₂+ €¦ + €¦ N_k= N. Suppose that a random sample of size n is selected, without replacement, from the population. Let X₁, X₂,€¦, X_kdenote the number of items of each type in the sample so that X₁+ X₂, + €¦ + €¦ + X_k= n. Show that for feasible values of n, x₁, x₂, €¦, x_k, N₁, N₂, €¦, N_k, the probability is

NE X1 P (X, = x,, X, = x,.., X, = x,) = C) X2 х,

NE X1 P (X, = x,, X, = x,.., X, = x,) = C) X2 ,

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