(Solved): Find E [Y] = ? (d) From the staircase CDF of Problem 3.4.1, we see that \( Y \) is a discrete ran ...

Find E [Y] = ?

(d) From the staircase CDF of Problem 3.4.1, we see that \( Y \) is a discrete random variable. The jumps in the \( \mathrm{CDF} \) occur at at the values that \( Y \) can take on. The height of each jump equals the probability of that value. The PMF of \( Y \) is \[ P_{Y}(y)=\left\{\begin{array}{ll} 1 / 4 & y=1 \\ 1 / 4 & y=2 \\ 1 / 2 & y=3 \\ 0 & \text { otherwise. } \end{array}\right. \]