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1. Let the random variable X denote the time (in hours) required to upgrade a computer...

1. Let the random variable X denote the time (in hours) required to upgrade a computer system. Assume that the probability density function for X is given by: p(x) = Ce^-2x for 0 < x < infinity (and p(x) = 0 otherwise).

a) Find the numerical value of C that makes this a valid probability density function.

b) Find the probability that it will take at most 45 minutes to upgrade a given system.

c) Use the definition of the expected value of X, to find the average time required to upgrade a computer system.

d) Find the moment generating function mx(t) for X, where t < 2.

e) Use your answer to part d) to verify your answer to part c)

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