Consider the following for the next four (04) items: Let (X1, X2, X3) be a random vector with the joint pmf given by: P(X1 = x1, X2 = x2, X3 = x3) = begincases 50!/x1!x2!x3!(50-x1-x2-x3)!(1/4)^x1(1/4)^x2(1/4)^x3(1/4)^50-x1-x2-x3 & if x1+x2+x3 le 50 0 & otherwise endcases The distribution of (50 - X1) is:

Q41Section I (Objective (Q1–Q80))41 of 80

Distribution Theory — marginal of a multinomial component

Consider the following for the next four (04) items: Let $(X_1, X_2, X_3)$ be a random vector with the joint pmf given by:

$\mathbb{P}(X_1 = x_1, X_2 = x_2, X_3 = x_3) = \begin{cases} \frac{50!}{x_1!x_2!x_3!(50-x_1-x_2-x_3)!}\left(\frac{1}{4}\right)^{x_1}\left(\frac{1}{4}\right)^{x_2}\left(\frac{1}{4}\right)^{x_3}\left(\frac{1}{4}\right)^{50-x_1-x_2-x_3} & \text{if } x_1+x_2+x_3 \le 50 \ 0 & \text{otherwise} \end{cases}$

The distribution of $(50 - X_1)$ is:

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