Answer: Show that the following function satisfies the

Chapter 5, Problem 101SE

(choose chapter or problem)

5-101.  Show that the following function satisfies the properties of a joint probability mass function:

0	0
0	1
1	0
1	1
2	2

 Determine the following:

(a) \(P(X<0.5, Y<1.5)\)
(b) \(P(X \leq 1)\)
(c) \(P(X<1.5)\)
(d) \(P(X>0.5, Y<1.5)\)
(e) \(E(X), E(Y), V(X), V(Y)\).
(f) Marginal probability distribution of the random variable
(g) Conditional probability distribution of  given that
(h) \(E(Y \mid X=1)\)
(i) Are  and  independent? Why or why not?
(j) Correlation between  and .

Equation transcription:

Text transcription:

P(X<0.5, Y<1.5)

P(X \leq 1)

P(X<1.5)

P(X>0.5, Y<1.5)

E(X), E(Y), V(X), V(Y)

E(Y \mid X=1)