A fair coin and a fair six-faced die are thrown simultaneously. The random variable $X$ is defined

Question

A fair coin and a fair six-faced die are thrown simultaneously. The random variable $X$ is defined as follows: If the coin shows a head, then $x$ is the score on the die. If the coin shows a tail, then $x$ is twice the score on the dice. Find $\mu$, the expected value of $X$ and show that $\mathrm{P}(X < \mu) = \frac{7}{12}$. Show that $\mathrm{Var}(X) = \frac{497}{48}$.

Accepted Answer

(i) $ \mu = \frac{21}{4} $.

Expected value and variance of a derived variable

Expected value and variance of a derived variable