Problem 1: A random variable X whose probability density function is given by fx(x) = 0.38(x-2)+ k tri (x²). Another random variable Yis related to X through Y= 2X-3. Find 1. The value of k 2. The expected value and the variance of X 3. The probability density function of Y. Problem 2: DRV X and Y have PDFs as fx(x) = 0.28(x) + 0.58(x-4) + 0.38(x-6) fy(y) = 0.58(x + 1) + 0.58(x-1) 1. What are the expected values E[X] and E[Y]? 2. What are the variances σ and o? 3. Assume a random variable Z = X + Y, what is the PDF of the random variable Z.

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