Interview Question: Another Density of Sum

Sample Question #180 (probability theory)

Consider two independent random variables X and Y. What’s the pdf of X+Y?

(Comment: how’s this question different from the previous one, #179?)

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One Response to Interview Question: Another Density of Sum

  1. Brett says:

    ANSWER
     
    The derivation is not quite straightforward, so you should just remember the result: the pdf of the sum of two independent variables is the convolution of their individual pdf’s. Let the two pdf’s be f(x) and g(y) respectively. The pdf of Z=X+Y is
     
       h(z) = integral (from -inf to +inf) { f(v)g(z-v) } dv
     
    More discussions can be found here.
     

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