Recent content by obst12

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    Calculate conditional expectation of exponential variables

    Awesome, thanks for all your help!
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    Calculate conditional expectation of exponential variables

    Thanks. Let me try once more. The joint density is ##abe^{-ax}e^{-by}## Then making the substitution ##X=Z## and ##Y=W-Z##. ##\rho_{Z.W}=abe^{-az}e^{-bw+bz}## ##\rho_{Z,W}=abe^{(b-a)z}e^{-bw}## Thus the marginal density is ##\rho_W=\int_0^w abe^{(b-a)z}e^{-bw} dz## ##\rho_W=abe^{-bw} \int_0^w...
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    Calculate conditional expectation of exponential variables

    Homework Statement Let X and Y be independent exponential random variables with parameters a and b. Calculate E(X|X+Y). Homework EquationsThe Attempt at a Solution I'm pretty sure I have it, just want to make sure. Joint density for X and Y is abe^(-ax)e^(-by) for x,y>0. Let Z=X and W=X+Y so...