Ans:
Let Mx(t) = 릉et + 24 + 킁e3. Find the following: (a) E(X) (b) Var(X) (c) If Y - X - 2, find the moment generating function of Y (d) If W -3X, find the moment generating function of W
1 point possible (graded) If Mx (t) = e-5(1-e'), find Var(X). Submit You have used 0 of 4 attempts Save
2. Let Mx(t) = 1c' + 2t?c". Find the following: (b) Var(X). (c) If Y = X-2, show that the moment-generating function of Y is e-2tMx(t). (d) If W = 3X, show that the moment-generating function of W is MX(3). 7/3,5/9
The mgf of X is Mx(t) = (¿e-* + ¿e Find P(X > -3|X < 2). -3t 0.86 0.17 0.91 none of the answers provided here 0.29 2) 5/6
in another word, find E[Yt] and var[Yt] t X be a random variable with mean 0 and variance σ2. Define Yİ = (-1)'X. Is this process stationary?
8. (10 pts.) The moment generating functions of X and Y are given by Mx(e) = (3x + 3) * and My (0) = + bene + cena respectively. Assuming that X and Y are independent, find (a) P{XY = 0} (b) P{XY >0} (c) Var (3X - 6Y + 2). (d) EXY.
11. Let Z = (X1,X2, X3)T be a portfolio of three assets. E(X) 0.50. E(X2-1.5. E(X3) = 2.5, VAR(X)-2, VAR(X2)-3, Var(Xs)-5·PX1.x2-0.6 and X1 and X2 are idependent of X3 (a) Find E(0.3xi +0.3X2 +0.4X3) and Var(0.3X1 +0.3X2 +0.4Xs) (b) Find P[0.3X1 +0.3x2 + 0.4X3 <2). Since z-table isn't provided, just write down the (c) Find the covariance between a portfolio that allocates 1/3 to each of the three assets and a portfolio that allocates 1/2 to each of the first...
The mgf of a random variable X has the following form: e-8t et 5 Mx(t) = 0.64 . Find ElYX). Answer:-0.2
Given f(x) = ( c(x + 1) if 1 < x < 3 0 else as a probability function for a continuous random variable; find a. c. b. The moment generating function MX(t). c. Use MX(t) to find the variance and the standard deviation of X.
Obtain E(Z|X), Var(Z|X) and verify that E(E(Z|X)) =E(Z), Var(E(Z|X))+E(Var(Z|X)) =Var(Z) 3. Let X, Y be independent Exponential (1) random variables. Define 1, if X Y<2 Obtain E (Z|X), Var(ZX) and verify that E(E(Zx)) E(Z), Var(E(Z|X))+E(Var(Z|X)) - Var(Z)