Please do by hand. Thanks in advance.
By the formula:
Var(aX - bY) = a2 Var(X) + b2 Var(Y) - 2*a*b*Cov(X, Y)
Hence,
Var(3Y - 2X) = 9*Var(Y) + 4*Var(X) - 2*3*2*Cov(X, Y) = 9*16 + 4*4 - 2*3*2*2 = 136
Please do by hand. Thanks in advance. 2. Let X and Y be two random variables....
Please do by hand. Thanks in advance. 1. Let X and Y be random variables with Var(X) = 4, Var(Y) = 9, and Var(X Y) = 10. What is Cov(X, Y)?
Please do by hand. Thanks in advance. 8. Let X and Y be random variables with a bivariate normal distribution with parameters • px = 5 • Ox= 3 • My = 3 • Oy = 2 • p=.4 a) Find the expected value and variance of Z=4X-Y. b) Find the covariance of X and Z. c) Identify the distribution of Y. d) Identify the distribution of Y|X = 5.
Let X and Y be two random variables such that: Var[X]=4 Cov[X,Y]=2 Compute the following covariance: Cov[3X,X+3Y]
9. Let X and Y be two random variables. Suppose that σ = 4, and σ -9. If we know that the two random variables Z-2X?Y and W = X + Y are independent, find Cov(X, Y) and ρ(X,Y). 10. Let X and Y be bivariate normal random variables with parameters μェー0, σ, 1,Hy- 1, ơv = 2, and ρ = _ .5. Find P(X + 2Y < 3) . Find Cov(X-Y, X + 2Y) 11. Let X and Y...
solution please 2. If X and Y are two random variables with Var(X) = 36, Var(Y) = 16, and Cov(X,Y) = 24, what is ρXY, the correlation coefficient between X and Y? (A) -1 (B) 0 (C) 1/24 (D) 1
Let X and Y be independent random variables with pdf 2-y , 0sys2 2 f(x) 0, otherwise 0, otherwise ) Find E(XY) b) Find Var (2X+3Y)
2. Let X and Y be two random variables with a joint distribution (discrete or continuous). Prove that Cov(X,Y)= E(XY) - E(X)E(Y). (15 points) 3. Explain in detail how we can derive the formula Var(X) = E(X) - * from the formula in Problem 2 above. (Please do not use any other method of proof.) (10 points)
Let X and Y be two independent random variables. Show that Cov (X, XY) = E(Y) Var(X).
Let X, Y be independent random variables with E[X] = E[Y] = 0 and ox = Oy = 5. Then Var(2x+3Y) = 1. True False
Let X, Y be independent random variables with E[X] = E[Y] = 0 and ox = oy = 5. Then Var(2x +3Y) = 1. True False