Answer:
(a) 1/3
(b) 1/15
Explanation:
(a)Let X denote the waiting time in minutes. It is given that X follows a uniform distribution, and since the variable being measured is time, we assume it to be a continuous uniform distribution.
![\[f_X(x) =\begin{cases} (1)/(30) & 0\leqx\leq 30\\ 0 & otherwise \end{cases}\]](https://img.qammunity.org/2021/formulas/mathematics/college/pw76t5hheyvj5jdfsl4hpqq2f971qjj5yj.png)
Now
.
Jack or Rose arriving first is equally likely, therefore the probability of Jack waiting is just the half of the above obtained probability i.e

(b)Using the formula for the expectation of a uniform continuous distribution,
