Chapter 5.1, Problem 1E

a.

To determine

Find the value of $P\left(X=1\text{ and }Y=1\right)$.

b.

To determine

Find the value of $P\left(X\le 1\text{ and }Y\le 1\right)$.

c.

To determine

Give a description of the event $\left\{X\ne 0\text{ and }Y\ne 0\right\}$ in words and compute the corresponding probability.

d.

To determine

Find the marginal pmf of X and Y.

Find the value of $P\left(X\le 1\right)$, using $p_X\left(x\right)$.

e.

To determine

Explain whether X and Y are independent random variables.