Chapter 7.2, Problem 27E

Table 17 gives the probability distribution of the random variable U.

Table 17

k	$\mathrm{Pr}\left(U=k\right)$
0	$\frac{4}{15}$
1	$\frac{2}{15}$
2	$\frac{4}{15}$
3	$\frac{3}{15}$
4	?

(a) Determine the probability that $U=4$.

(b) Find $\mathrm{Pr}\left(U\ge 2\right)$.

(c) Find the probability that U is at most 3.

(d) Find the probability that $U+2$ is less than 4.

(e) Draw the histogram of the distribution of U.