1 1 vote Let $X_{1}$ and $X_{2}$ be two independent continuous real-valued random variables taking values in the unit interval $[0,1]$. Let $Y=\max \left\{X_{1}, X_{2}\right\}$ and $Z=\left\{\begin{array}{ll}1 & \text { if } X_{1}=Y \\ 2 & \text { otherwise }\end{array}\right.$. Which of the following is true? $\operatorname{Pr}[Z=1]=\operatorname{Pr}[Z=1 \mid Y \geq 0.3] $ $\operatorname{Pr}[Z=1]=\operatorname{Pr}\left[Z=1 \mid Y=0.3, X_{1}=0.2\right]$ $\operatorname{Pr}[Z=1]=\operatorname{Pr}\left[Z=1 \mid Y=0.3, X_{1}=0.3, X_{2}=0.2\right]$ $\operatorname{Pr}[Z=1]>\operatorname{Pr}[Z=2]=\frac{1}{2}$ $\operatorname{Pr}[Z=1]<\operatorname{Pr}[Z=2]$ Probability and Statistics tifrece2016 probability-and-statistics random-variable + – admin 271 views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
