Chapter 7.2, Problem 29E

Table 19 gives the probability distribution of the random variable Y.

Table 19

k	$\mathrm{Pr}\left(X=k\right)$
1	.20
2	.20
3	.20
4	.40

(a) Draw the histogram for Y.

(b) Find $\mathrm{Pr}\left(Y=2\text{or}3\right)$

(c) Find the probability that $Y^2$ is at most 9.

(d) Find the probability that Y is at most 10.

(e) Find the probability distribution of ${\left(Y+2\right)}^2$.