1. Suppose that the moment generating function (MGF) of a random variable Y is m(t)= =...

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1. Suppose that the moment generating function (MGF) of a random variable Y is m(t)= = eet 1-t² > 0 is a known constant. Find m' (t) and E(Y). 2. Let m(t) = (2) et + (²) e²t. () e ³t. Find E(Y) and V(Y). 3. The length of time to failure (in hundreds hours) for a transistor is a random variable Y with distribution function given by 0 F(y) = {₁ - e-y² - iy <o : y20 a) Show that F(y) has the properties of a distribution function. b) Find f(y). c) Find the probability that the transistor operates at least 200 hours. 1. Suppose that the moment generating function (MGF) of a random variable Y is m(t)= = eet 1-t² > 0 is a known constant. Find m' (t) and E(Y). 2. Let m(t) = (2) et + (²) e²t. () e ³t. Find E(Y) and V(Y). 3. The length of time to failure (in hundreds hours) for a transistor is a random variable Y with distribution function given by 0 F(y) = {₁ - e-y² - iy <o : y20 a) Show that F(y) has the properties of a distribution function. b) Find f(y). c) Find the probability that the transistor operates at least 200 hours.

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