Two random variables X and Y are exponentially distributed with respective rates Ax = 1 and Ay = 2. Now, consider flipping a fair coin and observing the value of X if the outcome of the coin flip is Heads, and observing Y if that outcome is Tails instead. In other words, denoting the reported value as W, we have that W - X if Heads is observed, if Tails is observed. Construct the CDF of the random variable W, and use that to conclude that it has density given by fw (w) = = NIH [e-w + 2e 2w] for w > 0, and fw(w) = 0 otherwise. Hint: First show that P(W