Answer each question and label them with their corresponding letter or number. Show work.

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2. The lifetime in years of a manufactured product is Y = 5X^0.7, where X has an exponential distribution with mean 1. Find the cdf and pdf of Y.

3. Let X ? U (?1, 3). Find the PDF of Y = X^2.

4. Let X1 and X2 be independent random variables with respective binomial distributions Bin(3, 1/2) and Bin(5, 1/2). Determine: (a) P(X1 = 2, X2 = 4). (b) P(X1 + X2 = 7).

Let X have the pdf f(x) = xex2/2,0