Joint & marginal distributions

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Independent random variables $X$ and $Y$ are each discrete uniform: $X$ on $\{1, 2, \ldots, 6\}$ and $Y$ on $\{1, 2, \ldots, 3\}$, so all $18$ pairs $(X,Y)$ are equally likely. Find $P(X \le 5, Y \le 1)$, giving your answer as a fraction.

2. Warm-up

   Independent random variables $X$ and $Y$ are each discrete uniform: $X$ on $\{1, 2, \ldots, 6\}$ and $Y$ on $\{1, 2, \ldots, 5\}$, so all $30$ pairs $(X,Y)$ are equally likely. Find $P(X \le 5, Y \le 2)$, giving your answer as a fraction.

3. Warm-up

   Independent random variables $X$ and $Y$ are each discrete uniform: $X$ on $\{1, 2, \ldots, 6\}$ and $Y$ on $\{1, 2, \ldots, 6\}$, so all $36$ pairs $(X,Y)$ are equally likely. Find $P(X \le 6, Y \le 2)$, giving your answer as a fraction.

Problems shown under their original terms: Generated (template, solver-computed).