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Question 4 a) X and Y are two discrete random variables with joint probability function f(x,y) given by f(x,y) = (x+y)/32; x = 1, 2; y = 1, 2, 3, 4 i) Find the marginal p.f.’s of X and Y. [6] ii) Find P(X > Y). [5] iii) Find P(Y = 2X). [5] iv) Are X and Y independent? Give a reason for your answer. [2] b) Two continuous random variables X and Y have joint probability density function f(x,y) given by f(x,y) = { kx^2(1 + 2y); 0 ? x ? 2; 0 ? y ? 2; 0 otherwise i) Find the value of k. [5] ii) Find P(Y < 2X). [5] iii) Find E(XY). [5] iv) Find the marginal p.d.f.’s of X and Y. [6] v) Find Cov(X,Y). [5] vi) Are X and Y independent? Give a reason for your answer. [2]

          Question 4
a) X and Y are two discrete random variables with joint probability function f(x,y) given by
f(x,y) = (x+y)/32; x = 1, 2; y = 1, 2, 3, 4
i) Find the marginal p.f.’s of X and Y. [6]
ii) Find P(X > Y). [5]
iii) Find P(Y = 2X). [5]
iv) Are X and Y independent? Give a reason for your answer. [2]
b) Two continuous random variables X and Y have joint probability density function f(x,y) given by
f(x,y) = { kx^2(1 + 2y); 0 ? x ? 2; 0 ? y ? 2; 0 otherwise
i) Find the value of k. [5]
ii) Find P(Y < 2X). [5]
iii) Find E(XY). [5]
iv) Find the marginal p.d.f.’s of X and Y. [6]
v) Find Cov(X,Y). [5]
vi) Are X and Y independent? Give a reason for your answer. [2]

Question 4
a) X and Y are two discrete random variables with joint probability function f(x,y) given by
f(x,y) = (x+y)/32; x = 1, 2; y = 1, 2, 3, 4
i) Find the marginal p.f.’s of X and Y. [6]
ii) Find P(X > Y). [5]
iii) Find P(Y = 2X). [5]
iv) Are X and Y independent? Give a reason for your answer. [2]
b) Two continuous random variables X and Y have joint probability density function f(x,y) given by
f(x,y) = kx^2(1 + 2y); 0 ? x ? 2; 0 ? y ? 2; 0 otherwise
i) Find the value of k. [5]
ii) Find P(Y < 2X). [5]
iii) Find E(XY). [5]
iv) Find the marginal p.d.f.’s of X and Y. [6]
v) Find Cov(X,Y). [5]
vi) Are X and Y independent? Give a reason for your answer. [2]

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