Find the probability distribution of y

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Suppose that X denotes the years of education beyond high school and Y denotes the income in thousands. Suppose that we have the following joint probabilities:

P(X = 0, Y = 40) = 0.70
P(X = 0, Y = 80) = 0.05
P(X = 4, Y = 40) = 0.05
P(X = 4, Y = 80) = 0.20

(a) Find the probability distribution of Y.

(b) Find E(Y ) and V ar(Y ).

(c) Find P(Y = 40|X = 4) and P(Y = 80|X = 4).

(d) Find E(Y |X = 4) and V ar(Y |X = 4).

(e) Are X and Y independent? Explain.

Reference no: EM132841183

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