The random variable X is uniformly distributed over the interval [0, 5] and Y =
ID: 3391019 • Letter: T
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 =