Question: 6.16. A random experiment has four possible outcomes. Suppose that the experiment is re- peated n independent times and let Xx be the number of

6.16. A random experiment has four possible outcomes. Suppose that the experiment is re- peated n independent times and let Xx be the number of times outcome k occurs. The joint pmf of (X1, X2, X3) is given by n! 3! n + 3 p(k1, k2, k3) for 0 = k; and kj + k2 + k; = n. (n + 3)! 3 (a) Find the marginal pmf of (X1, X2). (b) Find the marginal pmf of X1. (c) Find the conditional joint pmf of ( X2, X3 ) given X, = m, where 0 s m s n

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