Question 7 M 0.3 Suppose the moment generating function for a random variable X is Mx(t) = 0.3 -t Let Y = 0.90X – 9. Determine the moment generating function of Y. 0.3 -9t A 0.3 -t 0.3 9t 0.3 -t в 0.3 -0.3t e 0.3 -t 1 -9t D 1- 3t

10 If 0₁ <0₂, derive the moment-generating function of a random variable that has a uniform distribution on the interval (0₁, 0₂). Suppose U has a uniform distribution on the interval (0₁, 0₂). Then, the moment generating function of U is derived as follows. mu(t)= E = = ·0₂ 7⁰2 du

part b

Let X; be random variables and M; (t) be their respective moment generating functions, for i = 1, 2, 3. Solve: Suppose that M₁ (t) = 1 +t+t² + t³+... Is this enough information to determine the type of random variable that X₁ is? Explain why or why not. Determine the type of random variable if there is enough information. Determine if it is possible for M₂ (t) = (-1)" -0 (2n)! possible, determine the type of random variable that X₂. -+2n. Explain why or why not. If it is Suppose that that the expectation of X3 is -1 and its second moment is 1. Determine if this is enough information to find the moment generating function of X3 explicitly. Explain why or why not. If it is enough information, compute it explicitly.