x={x1,x2,x3} has the 3-variate normal dustribution
with mean 0 and variance covariance matrix=(3 1 1
1 3 1
1 1 4)
find PDF of x in full
x={x1,x2,x3} has the 3-variate normal dustribution with mean 0 and variance covariance matrix=(3 1 1 &nbs
Q3. Assume that X- (X1, X2) is multivariate normal with mean zero and the variance-covariance matrix Let λ-(A1, λ2), Ai, A2 Value-at-Risk for Y 0, Ai + λ2-1. Let Y-Aix, + λ2Xy. Find the weights λι, λ2 that minimize
1. Suppose that X1, X2, and X3 E(X1) = 0, E(X2) = 1, E(X3) = 1, Var(X1) = 1, Var(X2) = 2, Var(X3) = 3, Cov(X1, X2) = -1, Cov(X2, X3) = 1, where X1 and X3 are independent. a.) Find the covariance cov(X1 + X2, X1 - X3). b.) Define U = 2X1 - X2 + X3. Find the mean and variance of U.
X1, X2, and X3 all have a normal distribution with mean 1 and variance 1. What is the variance of (2 X1 X2-X3)? 1 3 st
= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Yı, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fxı,Y,(y1, y2). iii) Suppose Y3 = X1 + X2 + X3. Compute the covariance...
Q1. Assume that (XiX2) is multivariate normal with mean vector (0,0) and the variance covariance matrix Find the VaRY(p) and ESY(p), where Y = X1 + X2.
Q1. Assume that (XiX2) is multivariate normal with mean vector (0,0) and the variance covariance matrix Find the VaRY(p) and ESY(p), where Y = X1 + X2.
Let X1 and X2 have joint PDF f(x1,x2)=x1+x2 for 0 <x1 <1 and 0<x2 <1.(a) Find the covariance and correlation of X1 and X2. (b) Find the conditional mean and conditional variance of X1 given X2 = x2.
I need the solution of this question asap
3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, 5. Let Var(x1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Y1, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fyy, y,(91, y2). iii) Suppose Y3 =...
Let x1, x2,x3,and x4 be a random sample from population with normal distribution with mean ? and variance ?2 . Find the efficiency of T = 1/7 (X1+3X2+2X3 +X4) relative to x= x/4 , Which is relatively more efficient? Why?
(12 points) The random variables X1, X2, and X; are jointly Gaussian with the following mean vector and covariance matrix: 54 2 07 2 5 -1 0-1 The random variable Y is formed from X1, X2, and X; as follows: Y=X1 - X2 + X3 +4. Determine P( Y> 3).
The matrix is the reduced echelon matrix for a system with variables x1, x2, x3, and x4. Find the solution set of the system. (If the system has infinitely many solutions, express your answer in terms of k, where x1 = x1(k), x2 = x2(k), x3 = x3(k),and x4 = k. If the system is inconsistent, enter INCONSISTENT.) 1 0 0 0 | −5 0 1 0 0 | 3 0 0 1 0 | −5 0 0 0 1...