Suppose X, Y are random variables with joint density f(x,y) = A^(3)xe^(-Ay) for 0<x<y = 0 otherwise a) What is the density of Y? What is E(Y)? b) What is E(X|Y=1)? -- thanks in advance for your help!
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Originally Posted by hanahou Suppose X, Y are random variables with joint density f(x,y) = A^(3)xe^(-Ay) for 0<x<y = 0 otherwise a) What is the density of Y? What is E(Y)? b) What is E(X|Y=1)? -- thanks in advance for your help! Marginal density: $\displaystyle f(y) = \int_0^y A^3xe^{-Ay}dx$ Expectation of Y: $\displaystyle E[Y] = \int_0^{\propto} y*f(y)dy$ For the second part, you need to find $\displaystyle f(x|y=1)$.
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