Methods of Multivariate Analysis textbook
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Methods of Multivariate Analysis textbook
4.17 Suppose y and x are subvectors, such that y is...
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y < (c) Find the margina...
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y < (c) Find the marginal pdf of X. (d) Find the conditional pdf of Y given that X = x. (e) Find E[Y IX x (f) Find E[E[YX]]. (g) Find Cov(X, Y) (h) Are X and Y independent?
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y
9. Let X and Y be two random variables. Suppose that σ = 4, and σ...
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...
The following relates to Problems 21 and 22. Let X ~ NĢi 1, σ2-1), Y ~ NĢı = 2,02-9) and ρχ.Y = 0.5 (recall that ρΧΥ stands for the correlation coefficient of X and Y) Problem 21: Find COV(X, Y) and...
The following relates to Problems 21 and 22. Let X ~ NĢi 1, σ2-1), Y ~ NĢı = 2,02-9) and ρχ.Y = 0.5 (recall that ρΧΥ stands for the correlation coefficient of X and Y) Problem 21: Find COV(X, Y) and Var(X +Y) 1 COV(X, Y) 1.5 and Var(XY)-15; [2] COV(X, Y) 3 and Var(X+Y)-7; 3 COV(X,Y) 3 and Var(X + Y) 10: 4] COV(X,Y) 1.5 and Var(X + Y)-7; [5] cov (X, Y) = 1.5 and Var (X +...
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z)...
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z) 4, V(Y) = 3 Let U X 3Y +Z and W = 2X + Y + Z 1, and Cov(X, Z) = -1 Compute E(U) and V (U) b. Compute Cov(U, W). а.
If the random variables X, Y, and Z have the means ji x = 3, My...
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 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. (b) Find the covariance of U and V.
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y...
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y, z) 1x2 + уг + z2 < 1} (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S....
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...
please asap 3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,' y. 0 0 1/12 1/6 1/24 7/2...
please asap
3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,' y. 0 0 1/12 1/6 1/24 7/24 1|¼ ¼ 1/40121/4。 2 Y 2 1/8 1/20 7/40 1/120 3 1/120 7/15 7/15 1/15!
3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,'...
1. Suppose you have two random variables, X and Y with joint distribution given by the...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
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.
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y < (c) Find the marginal pdf of X. (d) Find the conditional pdf of Y given that X = x. (e) Find E[Y IX x (f) Find E[E[YX]]. (g) Find Cov(X, Y) (h) Are X and Y independent?
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y
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...
The following relates to Problems 21 and 22. Let X ~ NĢi 1, σ2-1), Y ~ NĢı = 2,02-9) and ρχ.Y = 0.5 (recall that ρΧΥ stands for the correlation coefficient of X and Y) Problem 21: Find COV(X, Y) and Var(X +Y) 1 COV(X, Y) 1.5 and Var(XY)-15; [2] COV(X, Y) 3 and Var(X+Y)-7; 3 COV(X,Y) 3 and Var(X + Y) 10: 4] COV(X,Y) 1.5 and Var(X + Y)-7; [5] cov (X, Y) = 1.5 and Var (X +...
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z) 4, V(Y) = 3 Let U X 3Y +Z and W = 2X + Y + Z 1, and Cov(X, Z) = -1 Compute E(U) and V (U) b. Compute Cov(U, W). а.
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 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. (b) Find the covariance of U and V.
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y, z) 1x2 + уг + z2 < 1} (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S....
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...
please asap
3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,' y. 0 0 1/12 1/6 1/24 7/24 1|¼ ¼ 1/40121/4。 2 Y 2 1/8 1/20 7/40 1/120 3 1/120 7/15 7/15 1/15!
3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,'...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
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.
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