Show that the following function satisfies the properties of a joint probability mass function:

Determine the following:

(a) P(X <0.5, Y <1.5) 

(b) P(X ‰¤ 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 X

(g) Conditional probability distribution of Y given that X = 1

(h) E(Y |X = 1)

(i) Are X and Y independent? Why or why not?

(j) Correlation between X and Y.

Transcribed Image Text:

f(x, y) 1/4 1 1/8 1/8 1/4 1 2 1/4