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Let X and Y have joint probability density function f(x, y) = 2 I(0, 1)(x)I (0, 1)(y)I(0, 1)(x + y)
(a) Compute the marginal densities fx(x) and fy(y). Are X and Y independent?
Solution
f(x)= integration from (0 to 1-x) [ 2dy] = [2(1-x)]....
f(y)= integration from (0 to 1-y) [ 2dx] = [2(1-y)]....
f(x)*f(y) = [2(1-x)]* [2(1-y)] which is not equal to f(x,y)...so, they ar enot independent...

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Let X and Y have joint probability density function f(x, y) = 2 I(0, .pdf

  • 1. Let X and Y have joint probability density function f(x, y) = 2 I(0, 1)(x)I (0, 1)(y)I(0, 1)(x + y) (a) Compute the marginal densities fx(x) and fy(y). Are X and Y independent? Solution f(x)= integration from (0 to 1-x) [ 2dy] = [2(1-x)].... f(y)= integration from (0 to 1-y) [ 2dx] = [2(1-y)].... f(x)*f(y) = [2(1-x)]* [2(1-y)] which is not equal to f(x,y)...so, they ar enot independent...