For random variables X, Y, and Z, Var(X) = 4, Var(Y) = 9, Var(Z) = 16, E[XY] = 6, E[XZ] = −8, E[Y Z] = 10, E[X] = 1, E[Y ] = 2 and E[Z] = 3. Calculate the followings:
(b) Cov(−3Y , −4Z ).
(d) Var(Y − 3Z).
(e) Var(10X + 5Y − 5Z).
For random variables X, Y, and Z, Var(X) = 4, Var(Y) = 9, Var(Z) = 16,...
(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).
X,Y, and Z are random variables. Var(X) = 2, Var(Y) = 1, Var(Z) = 5, Cov(X,Y) = 3, Cov(X, Z) = -2, Cov(Y,Z) = 7. Determine Var(3X – 2Y - 2+10)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. ar (x) 34 Var (Y)- Var() 35 Compute the values of the expressions below. E 4 + 5Z2) -4Z-5x -О Var (-5Y+2)
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]
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)-8 E(Y)-7 E(Z)-2 Var (x) 24 Var (Y) 2 Var (z) 29 Compute the values of the expressions below. E (5x- 4) Var (-2 5z) - [D
Let X and Y be random variables with the follow E(Y) μ,--2 Var(x) o, 0.3 Var(Y)-σ,-0.5 Cov(XY) o,,-0.03 Find the following: ESX-3 Y)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-4 E(Y) 2 E(Z)-7 Var (x) -28 Var(Y)-3 Var (Z) -44 Compute the values of the expressions below. E(Y 1) 5Z + 4x Var (4Y-3)
4. Recall that the covariance of random variables X, and Y is defined by Cov(X,Y) = E(X - Ex)(Y - EY) (a) (2pt) TRUE or FALSE (circle one). E(XY) 0 implies Cov(X, Y) = 0. (b) (4 pt) a, b, c, d are constants. Mark each correct statement ( ) Cov(aX, cY) = ac Cov(X, Y) ( ) Cor(aX + b, cY + d) = ac Cov(X, Y) + bc Cov(X, Y) + da Cov(X, Y) + bd ( )...
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-3 E(Y)9 E(Z)-2 Var(X) = 36 par(r)=19 par(Z)-10 Compute the values of the expressions below E (32 +3) 5Y+ 2x Var (5-2)-
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