For the random variables X and Y having E(X) = 1, E(Y) = 2, Var (X)...
Show steps, thanks ·Additional Problem 13. For random variables X and Y it is given that Ox = 2, ơY = 5, and pxy 3 (a) Find Cov(Xx,y) (b) Var(4X-2Y7 Answers: (a) -. (b) 002 10652 li 3 . Additional Problem 14. Suppose Xi and X2 are independent random variables that have exponential distribution with β 4. (a) Find the covariance and correlation between 5Xi + 3X, and 7Xi-2X. (b) Find Var-5X2-2
Let X and Y be jointly continuous random variables having joint density fxy(x,y) = 2 y + x1, x>0, y> O otherwise Find Cov(X,Y) and Determine the correlation coefficient PXY O A. Cov(X,Y) = -1/36 , PXY=-1/2 OB. Cov(X,Y) = -1/18, PXY= 1/3 OC. Cov(X,Y) = -1/36 , PXY=0 OD. Cov(X,Y) = 1/12, PXY--1/2
= Var(X) and σ, 1. Let X and Y be random variables, with μx = E(X), μY = E(Y), Var(Y). (1) If a, b, c and d are fixed real numbers, (a) show Cov (aX + b, cY + d) = ac Cov(X, Y). (b) show Corr(aX + b, cY +d) pxy for a > 0 and c> O
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
Suppose X andY are two random variables withE[X]=1,Var(X)=4,E[Y]=−1,Var(Y)=4,andCov(X,Y)=1. Find: (a) correlation between X and Y . (b) Var(X −Y).
6 Suppose that X and Y are random variables such that Var(X) Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y+2)
6 Suppose that X and Y are random variables such that Var(X)-Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y + 2)
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).
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
O. Let X1 and X2 be two random variables, and let Y = (X1 + X2)2. Suppose that E[Y ] = 25 and that the variance of X1 and X2 are 9 and 16, respectively. O. Let Xi and X2 be two random variables, and let Y = (X1 X2)2. Suppose that and that the variance of X1 and X2 are 9 and 16, respectively E[Y] = 25 (63) Suppose that both X\ and X2 have mean zero. Then the...