II. (50%) 1. (15%) Suppose $X$, $Y$, and $Z$ are independent Poisson random variables, each with mean 1. Find a. $P(X+Y+Z=4)$ b. $E[(X+Y)^2]$ c. $P\left(X=1 \mid \frac{X+Y}{2} = 2\right)$
阿摩線上測驗
登入
阿摩線上測驗
登入
II. (50%) 1. (15%) Suppose $X$, $Y$, and $Z$ are independent Poisson random variables, each with mean 1. Find a. $P(X+Y+Z=4)$ b. $E[(X+Y)^2]$ c. $P\left(X=1 \mid \frac{X+Y}{2} = 2\right)$