Chapter 4.4, Problem 4.65LM

a.

To determine

$P\left(x\le 2\right)$ when $\lambda =1$.

b.

To determine

$P\left(x\le 2\right)$ when $\lambda =2$.

c.

To determine

$P\left(x\le 2\right)$ when $\lambda =3$.

d.

To determine

The nature of change in the probability of the event $\left\{x\le 2\right\}$ as $\lambda$ increases from 1 to 3 and whether it is intuitively reasonable.