2. Let X be a uniform random variable over the interval (0, 1).Let Y = X(1-X). a. Derive the pdf for Y . b. Check the pdf youfound in (a) is a pdf. c. Use the pdf you found in (a) to find themean of Y . d. Compute the mean of Y by using the distribution forX. e. Use the pdf of Y to evaluate P(|x-1/2|<1/8). You cannotuse the pdf for X. f. Use the pdf of X to evaluateP(|X-1/2|<1/8).
