Introduction to Probability · Problem 4.1.39

Conditional Probability — Grinstead & Snell

Mathematics — Probability · joint-distribution

Problem

Assume that the random variables

X

and

Y

have the joint distribution given in Table 4.6. (a) What is

P(X \ge 1

and

Y \le 0)

? (b) What is the conditional probability that

Y \le 0

given that

X = 2

? (c) Are

X

and

Y

independent? (d) What is the distribution of

Z = XY