Assume X, Y are independent with EX = 1 EY = 2 Var(X) = 22 Var(Y) = 32 Let U = 2X + Y and V = 2X – Y. (a) Find E(U) and E(V). (b) Find Var(U) and Var(V). (c) Find Cov(U,V).
(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).
6. Show that Var[X] = E[X2], if EX] = 0.
6. Let X be an exponential random variable with parameter 1 = 2. Compute E[ex]. = 7. Consider a random variable X with E[X] u and Var(X) 02. Let Y = X-4. Find E[Y] and Var(Y). The answer should not depend on whether X is a discrete or continuous random variable.
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]
For the random variables X and Y having E(X) = 1, E(Y) = 2, Var (X) = 6, Var (Y) = 9, and Pxy = -2/3. Find a) The covariance of X and Y. b) The correlation of X and Y. c) E(X2) and E(Y2).
Suppose X ∼ N(0, 1). (1) Explain the density of X in terms of the diffusion process. (2) Calculate E(X), E(X^2 ), and Var(X). (3) Let Y = µ + σX. Calculate E(Y ) and Var(Y ). Find the density of Y.
QUESTION 9 Given E(X)=2 and Var(X)=4, let Y =5X-3. Find E(Y) Var(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.
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.