4.2.1 problem 20

(a)

This is not possible, since $Y$ has a non-zero probability of being a number larger than $100$, where as $X$ is capped at $100$.

(b)

Let $X$ be the number of contestants who enter a tournament, and let $Y$ be the number of contestants who pass the first round. Clearly, $P(X\ge Y)=1$.

(c)

This is not possible, because if $X$ always produces values smaller or equal to the values produced by $Y$, then $\text{E}\left(X\right)\le \text{E}\left(Y\right)$. However, $\text{E}\left(X\right)=90$, and $\text{E}\left(Y\right)=50$.