Setup:

We are given a stick that extends from 0 tox. Its length,x, is the realization of an exponential random variableX, with mean1. We break that stick at a pointY, that is uniformly distributed over the interval[0, x].

Question:

Find Var(E[Y|X]) = ?

We are given a stick that extends from O 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.Write down the (fully specified)joint PDF fX,Y (x, y) of X and Y. For0