If the random variables X, Y, and Z have the means ji x = 3, My...

Question

Question

If the random variables X, Y, and Z have the means ji x = 3, My = -2, and uz = 2, the variances of = 3, o = 3, o2 = 2, the co

Answer 1

Answer #1

3 -3 Cov ( z and Cov(Y)a とニ 9 CovlY2) U- y-Z V X-y+Z NY-HZ 3-(a(a) Vasiance ef u : 3+2 0JCov(xa) - 3 3 a- 2(-2)+4--4() 16 **

Answer 2

Similar Homework Help Questions

If the random variables X, Y, and Z have the means ux = 3, uy =...

If the random variables X, Y, and Z have the means ux = 3, uy = -2, and uz = 2, the variances o = 3, o = 3, o2 = 2, the covariances cov(X,Y) = -2, cov(X, Z) = -1, and cov(Y,Z) = 1, U = Y - Z, and V = X - Y +2Z. (a) Find the mean and the variance of U and V, respectively. (b) Find the covariance of U and V.
5. The means, standard deviations, and covariance for random variables X, Y, and Z are given...

5. The means, standard deviations, and covariance for random variables X, Y, and Z are given below. Ux= 3, uy = 5, uz = 7 Ox= 1, OY = 3, oz = 4 cov(X, Y) = 1, cov (X, Z) = 3, and cov (Y,Z) = -3 T= X-28 +3 Z var(T) = 16. For a random variable X with an unknown distribution. The mean of X is u = 22 and tting a randomly chosen value of X
Suppose the random variables X, Y and Z are related through the model Y = 2...

Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + Z, where Z has mean 0 and variance σ2 Z = 16 and X has variance σ2 X = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X, Y ) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter 4. Suppose the...

5. Suppose the random variables X, Y and Z are related through the model Y =...

5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + 2, where Z has mean 0 and variance o2 = 16 and X has variance of = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X,Y) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter
5. Suppose the random variables X, Y and Z are related through the model Y =...

5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + Z, where Z has mean 0 and variance o2 = 16 and X has variance of = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X, Y) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter
14. Random variables X and Y have a density function f(x, y). Find the indicated expected...

14. Random variables X and Y have a density function f(x, y). Find the indicated expected value. f(x, y) = (xy + y2) 0<x< 1,0 <y<1 0 Elsewhere {$(wyty E(x2y) = 15. The means, standard deviations, and covariance for random variables X, Y. and Z are given below. LIX = 3. HY = 5. Az = 7 Ox= 1, = 3, oz = 4 cov(X,Y) = 1, cov (X, Z) = 3, and cov (Y,Z) = -3 T = X-2...

15. The means, standard deviations, and covariance for random variables X, Y. and Z are given...

15. The means, standard deviations, and covariance for random variables X, Y. and Z are given below. x = 3, uy = 5. z = 7 ox= 1, OY = 3, oz = 4 cov(X, Y) = 1, cov (X, Z) = 3, and cov (Y,Z) = -3 T=X-2Y+3 Z var(T) =
Problem 3: 10 points σ2. Define Assume that U, V, and W are independent random variables...

Problem 3: 10 points σ2. Define Assume that U, V, and W are independent random variables with the same common variance X= + W and Y-V-W. 1. Find the variances Var[X] and Var[Y 2. Find the covariance between X and Y, that is: cov [x,Y 3. Find the covariance between (X+Y) and (X - Y), that is: COV[(X +Y), (X -Y)]
The joint probability density function is f(x, y) for 17. Find the mean of X given...

The joint probability density function is f(x, y) for 17. Find the mean of X given Y = random variables X and Y fax, y) = f(xy *** Q<x<10<x<1 Elsewhere w 14. Random variables X and Y have a density function f(x, y). Find the indicated expected value f(x, y) = 6; (xy+y4) 0<x< 1,0<y<1 0 Elsewhere E(x2y) = 15. The means, standard deviations, and covariance for random variables X, Y, and Z are given below. Lex= 3, uy =...

Use this result without proof: if X and Y are two normal random variables with means...

Use this result without proof: if X and Y are two normal random variables with means ux and My respectively, and variances oź and oſ respectively, and Z = X+Y, Z is also a normal random variable with mean (ux + Hy) and variance (ox +og). a) Suppose Yı, Y2, Yz, Y4 and Y5 are all independent normal random variables, each with a mean of 1 and a variance of 5. What is the probability that (Y1 + 2Y2 +...