Consider a random variable, W, with the moment generating function Mw(t) = (0.1 + 0.9e¹)2. Determine the third moment, E[W³].
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- A random variable, H, has the moment generating function, My(t) = e¹2e¹-12. De- termine the second moment of the random variable H, E[H²].TF.12 The joint pdf of the lifetimes X and Y in years of two batteries working in parallel is (see picture) a) Find the probability P(Y ≤ 0.5). b) Find the expected values E(X) and E(XY).Let Y be a random variable with moment-generating function m(t) = ¿e=t + } + tet, where -0Given that the discrete random variable X has the moment generating function 0.2et Mx(t) 1-0.8et find the pmf of X.The random variable U has the following distribution: U 123 PU(u) 0.20 0.40 0.40 (c) Write down the moment generating function (mgf) of U. (d) Use the mgf to help determine var[U].Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.Your internal body temperature T in °F is a Gaussian (μ =98.6, σ = 0.4) random variable. In terms of the Φ function, find P[T > 100]. Does this model seem reasonable?Let a, µ E R. Calculate f exp{-ax²/2+µx}dx. (Hint: recall that the PDF for a normal random variable Z ~ N(H, o2) is p(2) = (270²)-1/2 exp{-(z – µ)²/(20²)} and that p(z)dz = 1.)Find E[XY] if fxr) = 2/3 and the joint PDF of the random variables X and Y is zero outside and constant on the shaded region y 2-SEE MORE QUESTIONS