$$
\begin{aligned}
P(Y=k) & = \begin{cases}\frac{1}{101} & \text { if } k=0 \\
\frac{2}{101} & \text { if } 1 \leq k \leq 50\end{cases} \\
E(Y) & =\sum_{k=0}^{50} k \cdot P(Y=k) \\
& =0 \cdot \frac{1}{101}+\sum_{k=1}^{50} k \cdot \frac{2}{101} \\
& =\frac{2}{101} \sum_{k=1}^{50} k \\
& =\frac{2}{101} \cdot 1275 \\
& =\frac{2550}{101}
\end{aligned}
$$
