Question: 2. Exponentials [10 points Recall that for two independent random variables X and Y with PDFs fx and fy, respec- tively, the joint PDF of

2. Exponentials [10 points Recall that for two independent random variables

2. Exponentials [10 points Recall that for two independent random variables X and Y with PDFs fx and fy, respec- tively, the joint PDF of X and Z, where Z = X + Y, is given by fxz(x, z) = fx(x) fy(z -x). Consider two independent exponential random variables X1 and X2 with parameter 1. Let Y1 = X1, Y2 = X1 + X2. Find the MMSE estimate of Y1 using Y2

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