Hi! I appreciate your help with the result and approach for these questions. Thanks!

Mid Term due Jul 20, 2021 18:59 CDT Problem 2 3.0 points possible (graded, results hidden) 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 (O, c]. 1. Write down the (fully specified) joint PDF fx,y- (x, y) of X and Y. For O < y S c: fx,Y (c, Y) = 2. Find X]). 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 MAP estimate of X: STANDARD NOTATION