The random variable X is uniformly distributed over the interval [0, 5] and Y =

Question

The random variable X is uniformly distributed over the interval [0, 5] and Y = (X + 2)^2. Find the mean of X, mux, the standard deviation of X, sigmax . Find the PDF of Y, fY(y). Find the mean of Y, muY, using three methods: Directly from the moments of X. Indirectly from E[g(X)]= +infinity integrate -infinity g(x)fx(x)dx. Directly from the definition muy = E[Y] = +infinity integrate -infinity y fY (y) dy. Approximately using a second-order approximation. What is the error of this approximation (in percent)?

Explanation / Answer

The random variable X is uniformly distributed over the interval [0, 5] and Y =

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