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5. Let X be a uniform random variable in (0,1) and let Y be a gamma random variable with shape
parameter 2 and scale parameter 1/3. Define U=XY (a) Show that the characteristic function of U
is given by U(t)=1it/31,tR (b) Hence, find the mean and variance of U. (c) Show that P(U2)1/18

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  • 1. 5. Let X be a uniform random variable in (0,1) and let Y be a gamma random variable with shape parameter 2 and scale parameter 1/3. Define U=XY (a) Show that the characteristic function of U is given by U(t)=1it/31,tR (b) Hence, find the mean and variance of U. (c) Show that P(U2)1/18