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Let X be a random variable with the moment generating function m() Show that the moment generating fenction Y = a X tb is given by I'm (at), and use this to show E ( Y) = a Eco + b. 2.) for each part, find the distribution and the expected value of the random variable with the given moment generating function. a) mx (t ) = (0.3 et + 0.7) 6 6) mx (t) = 0,2 + 0.38 to. ye + oil Suppose that we toss a fair coin three times. Let X denote the # of heads observed. a Find the values of / ##= EC x) and 0 2= var (x) D Find the exact value of P(/ X-/