Originally Posted by

**downthesun01** *Consider n multinomial trials, where each trial independently results in outcome i with probability $\displaystyle p_i,\sum_{i=1}^{k}p_{i}=1$. With $\displaystyle X_i$ equal to the number of trials that result in outcome i, find $\displaystyle E[X_{1}|X_2>0].$*

I'm having a hard time understanding what the question is asking. Am I looking for the average number of trials that result in $\displaystyle X_1$ given that there's at least one trial that results in $\displaystyle X_2$?

To work out the conditional expectation you need the conditional probability:

EDIT:

After thinking about it, isn't the answer just

$\displaystyle 1-n\sum^{k}_{i=2}p_i$

I don't know, I don't think I'm getting the question.