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 <0.5)

(c) P(Y <1.5) 

(d) P(X >0.25, Y < 4.5)

(e) E(X ), E(Y ), V (X ), and V (Y )

(f) Marginal probability distribution of X

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

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

(i) E(X | y = 1) 

(j) Are X and Y independent?

Transcribed Image Text:

fxy (x, y) 1/8 1/4 1/2 1/8 х -2 -2 -1 -1.0 -0.5 0.5 1 1.0