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Let X and Y be two independent random variables such that X + Y has the...

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Basic Math

Let X and Y be two independent random variables such that X + Yhas the same density as X. What is Y?

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3.8 Ratings (344 Votes)
A generalised case Suppose X and Y are two independent random variables with density functions ie pdfs fxx and fyy Let ZXY Suppose X takes some specific value integer m Then Zz iff Yzm So the event Z is the union of two disjoint events Xm and Yzm note that when two events are independent PABPAPB PZz PxxPYy the    See Answer
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