A system for a random amount of time X (in units of months) is given by a density Stxe*² ; x>0, f(x)= ; x<0. Find the moment generating function of X. Hence, compute the variance of Х. (а) (b) Deduce the expression for the k th moment. 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. (c)

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