Suppose that EX-EY-0, var(X) = var(Y) = 1, and corr(X,Y) = 0.5. (i) Compute E3X -2Y]; and (ii) var(3X - 2Y) (ii) Compute E[X2]
7. Show that σ2 E(X-0 and Var(X if X1, . . . , Xn are independent and identically distributed with E(Xi) = 0 and E(X2) = σ2 for i = 1,-.. , n
8. With K(t) = ln(EetX), show that k'(0)-EX], K"(0) = Var(X).
E(X) 2 and EX(X - 1))-5. Find Var(X)
(2. Assume that X, Y, and Z are random variables, with EX) = 2, Var(X) = 4, E(Y) = -1, Var(Y) = 6, E(Z) = 4, Var(Z) = 8,Cov(X,Y) = 1, Cov(X, Z) = -1, Cov(Y,Z) = 0 Find E(3X + 4y - 62) and Var(3x + 4y - 62).
Problem 4 Suppose X ~N(0, 1) (1) Explain the density of X in terms of diffusion process. (2) Calculate E(X), E(X2), and Var(X). (3) Let Y = μ +ơX. Calculate E(Y) and Var(Y). Find the density of Y. Problem 4 Suppose X ~N(0, 1) (1) Explain the density of X in terms of diffusion process. (2) Calculate E(X), E(X2), and Var(X). (3) Let Y = μ +ơX. Calculate E(Y) and Var(Y). Find the density of Y.
1. Suppose (x, Y) has bivariate normal distribution, E(x) E(Y)- 0, Var(X) σ , Var(Y) σ and Correl(X, Y) p. Calculate the conditional expectation E(X2|Y).
1 pts Question 3 Var(x2) 5, and E(x4)= 14. What is var(X) (the answer is an integer)? You are told that E (X) = 1. 1 pts Question 3 Var(x2) 5, and E(x4)= 14. What is var(X) (the answer is an integer)? You are told that E (X) = 1.
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...
2. (7 pt) Recall that the variance of a random variable X is defined by Var(X) - E(X - EX)2. Select all statements that are correct for general random variables X,Y. Throughout, a, b are constants. ( Var(X) E(X2) (EX)2 ( ) Var(aX + b) = a2 Var(X) + b2 Var(aXb)a Var(X)+b ( ) Var(X + Y) = Var(X) + Var(Y) ) Var(x) 2 o ) Var(a)0 ( ) var(x") (Var(X))"