# Joint Probability

3. The joint probability density function of X and Y is given by

f(x, y) =6/7 (x2 + xy/2 ), 0 < x < 1, 0 < y < 2.

(a) Verify that this is indeed a joint density function.

(b) Compute the density function of X.

(c) Find P(X > Y ).

(d) Find P(Y > 1/2|X < 1/2).

(e) Find E(X).

(f) Find E(Y ).

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#### Solution Summary

3. The joint probability density function of X and Y is given by

f(x, y) =6/7 (x2 + xy/2 ), 0 < x < 1, 0 < y < 2.

(a) Verify that this is indeed a joint density function.

(b) Compute the density function of X.

(c) Find P(X > Y ).

(d) Find P(Y > 1/2|X < 1/2).

(e) Find E(X).

(f) Find E(Y ).

Probability Tree & Joint Probability Table

A retail outlet receives radios from three electrical appliance companies. The outlet receives 20% of its radios from A, 40% from B, and 40% from C. The probability of receiving a defective radio from A is .01; from .02; and from C .08.

A. Develop a probability tree showing all marginal, conditional and joint probabilities.

B. Develop a joint probability table.