Question: The random variable X is uniformly distributed over the interval (0, 5) and Y = 2(X +2). (a) Find the mean of X, ux, the

The random variable X is uniformly distributed over the interval (0, 5) and Y = 2(X +2). (a) Find the mean of X, ux, the standard deviation of X, ox. (b) Find the PDF of Y, fy (y) . (c) Find the mean of Y, my, using three methods: (i) Directly from the moments of X too (ii) Indirectly from E g(X)] = [ g(x) fx (x) dx -00 (iii) Directly from the definition My = E[Y] = Syfy (y) dy -co (iv) Approximately using a second-order approximation. What is the error of this approximation (in percent)

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