A system for a random amount of time X (in units of months) is given by a density xe 2 ; x>0, S(x)=xe- ; x<0. (a) Find the moment generating function of X. Hence, compute the variance of Х. (b) Deduce the expression for the k th moment. (c) Obtain the distribution function of X . Hence, compute that the probability that, 7 of such system, at least 4 will function for at least 6 units of months. State the assumptions that you make.

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