[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Assume that the random variables [math]X[/math] and [math]Y[/math] have the joint distribution

given in Table.

Joint distribution.

		[math]Y[/math]
		-1	0	1	2
[math]X[/math]	-1	0	1/36	1/6	1/12
	0	1/18	0	1/18	0
	1	0	1/36	1/6	1/12
	2	1/12	0	1/12	1/6

• What is [math]P(X \geq 1\ \mbox {and\ } Y \leq 0)[/math]?
• What is the conditional probability that [math]Y \leq 0[/math] given that [math]X = 2[/math]?
• Are [math]X[/math] and [math]Y[/math] independent?
• What is the distribution of [math]Z = XY[/math]?