Question: We are given a stick that extends from 0 to x . Its length, x , is the realization of an exponential random variable X

We are given a stick that extends from 0 to x . Its length, x , is the realization of an exponential random variable X , with mean 1 . We break that stick at a point Y that is uniformly distributed over the interval [0,x] .

1. Find joint PDF fX,Y(x,y) of X and Y . For 0

2. Var(E[YX]) :

3. We do not observe the value of X , but are told that Y=2.2 . Find the MAP estimate of X based on Y=2.2 .Find MAP estimate of X :

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