Suppose a trial can result in precisely one of k mutually exclusive eventsA 1 ,
Question:
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 tria...View the full answer
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