Suppose a trial can result in precisely one of k mutually exclusive eventsA 1 , ,A k with probabilities p 1 , , p k , respectively, where P 1 + + P k = 1. Suppose that n independent trials are performed. Show that the probability of getting x 1 A 1
Chapter 24, PROBLEM SET 24.7 #17
Suppose a trial can result in precisely one of k mutually exclusive events A1, · · ·,Ak with probabilities p1, · · ·, pk, respectively, where P1 + · · · + Pk = 1. Suppose that n independent trials are performed. Show that the probability of getting x1A1’s, · · ·, xkAk's is
where 0 ≤ xj ≤ n, j = 1, · · ·,k, and x1 + · · · + xk = n. The distribution having this probability function is called the multinomial distribution.
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We can approach this problem using the following reasoning: Consider a sequence of n independent tri…View the full answer
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