2. Let X be a uniform random variable over the interval (0, 1).
Let Y =...
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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).
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a We have Y X1XSo as X Unif01 X01 X1X X 0We first find cdf of Y1 PX is in between the roots
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