(a)[2]
Show that, by calculation, $P(X = 3) = \frac{7}{15}$.
(b)[3]
Construct the probability distribution table for $X$.
(c)[3]
Find both $\text{E}(X)$ and $\mathrm{Var}(X)$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
One fair three-sided spinner is labelled 1, 2, 3. Another fair five-sided spinner is labelled 1, 1, 2, 2, 3. Each spinner is spun once, and the number showing on the side where it lands is recorded. The random variable $X$ is the larger of the two numbers when they are different, and their shared value when they are the same.