Using the formula for the multinomial distribution, the probability of X1 = 2, X2 = 2, X3 = 1 when n = 5, p1 = 0.4, p2 = 0.5, p3 = 0.1 is
A)0.0600
B)0.0900
C)0.1200

Question

Quizplus · Accepted Answer

The formula for the multinomial distribution is:
P(X1 = x1, X2 = x2, ..., Xk = xk) = n!/(x1!x2!...xk!) p1^x1 * p2^x2 * ... * pk^xk
where n is the total number of trials, xi is the number of trials in the i-th category, pi is the probability of success in the i-th category, and k is the number of categories.

In this case, we have k = 3, n = 5, x1 = 2, x2 = 2, x3 = 1, p1 = 0.4, p2 = 0.5, and p3 = 0.1. Plugging these values into the formula, we get:

P(X1 = 2, X2 = 2, X3 = 1) = 5!/2!2!1! (0.4)^2 * (0.5)^2 * (0.1)^1 = 0.12

Therefore, the answer is C.

Using the Formula for the Multinomial Distribution, the Probability of X1