5, Let the continuous random variable X denote the time required {in hours) to upgrade a computer system- Suppose that the probability density function forX is given by: 3: PH) = C ' 6 forx 3- {} {and 0 otherwise). (a) Find the value for the constant c that makes this a valid probability density function. (h) Calculate the probability that it takes between 30 and 40 minutes to upgrade the computer system. (c) Find, using the denition of expected value, the average time that it takes to upgrade the computer system. {d} Show that the moment generating function forX is equal to 3f[3-t] for t