Suppose two discrete random variables x and y each take only the values 1,2, and

Question

Suppose two discrete random variables x and y each take only the values 1,2, and 3. Assume the joint density function is described P = [ 0.03 0.02 0.05 ] [ 0.15 0.1 0.25 ] [ 0.12 0.08 0.2 ] Where the i-th column/row corresponds to the value i with i = 1,2,3 (a) compute P(xy >=4) (b) compute the marginal densities for x and y (c) Are these random variables independent > explain

Explanation / Answer

a) P(XY >=4) =>. x = 2 0r 3 , y = 2 or 3 = 0.1 + 0.25 + 0.08 + 0.2 = 0.63 b) fx(X) = 0.1 for x = 1 0.5 for x=2 0.4 for x = 3 fy(Y) = 0.3 for y=1 0.2 for y =2 0.5 for y=3 c) fx(X)*fy(Y) = 0.03 for x=1 y=1 = 0.02 for x=1 y=2 = 0.05 for x=1 y=3 = 0.15 for x=2 y=1 = 0.1 for x=2 y=2 = 0.25 for x=2 y=3 = 0.12 for x=3 y=1 = 0.08 for x=3 y=2 = 0.2 for x=3 y=3 since fx(X)*fy(Y)= f(X,Y) x,y are independent

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