a)
f(Y|X = x) = f(x,y) / f(x)
f(Y|X = x) = 4/5 (x+y) /x^3 / ((4x+2)/5x^3 )
= 4 (x+y)/(4x+2)
f(Y | X = 2) = 4(2 +y)/10) = 0.4 * (y+5)
P(0 <Y< 1/2 |X = 2) =
b)
P( 0 < Y <1/2 |X> A) = 5/16
P(0 < Y < 1/2 and X > A) / P(X > A) = 5/16
P(0 < Y < 1/2 and X > A) =
P(X>A) =
hence
P( 0 < Y <1/2 |X> A) = 5/16
((8a+ 1)/20a^2 ) /((4A + 1)/5A^2 ) = 5/16
a = 1/12
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Problem 7: Let X and Y be two jointly continuous random variables with joint PDF 4...
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