Question: Show that the following function satisfies the properties of a joint probability mass function. Determine the following: (a) P(X <2.5, Y <3) (b) P(X <2.5)

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

y fxr (x, y) 1.0 1 1/4 1.5 2 1/8 1.5 3 1/4 2.5 4 1/4 3.0 1/8

Determine the following:

(a) P(X <2.5, Y <3) (b) P(X <2.5)

(c) P(Y <3) (d) P(X >1.8, Y > 4.7)

(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 = 1.5

(h) Conditional probability distribution of X given that Y = 2

(i) E(Y | X = 1.5) 

(j) Are X and Y independent?

y fxr (x, y) 1.0 1 1/4 1.5 2 1/8 1.5 3 1/4 2.5 4 1/4 3.0 1/8

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