Q3. Assume that X- (X1, X2) is multivariate normal with mean zero and the variance-covariance matrix...
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, x2 denote the variables for the two-dimensional data summarized by the covariance matrix, the eigenvalues, and the unit eigenvectors shown below. Find a new variable y, of the form y 1 +ewh2-1, such that y, has maximum possible variance over the given data. How much of the variance in the data is explained by y,? 74.968-14.032. λι 78.245, 0.23 -0.97 u,-| and λ,-14.891, u,- 0.23 14.032 18.168 -0.97 Let x1, x2 denote the variables for the two-dimensional data...
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
Given a data matrix X as in Question 2, Assume the means of the p variables are zero. Let S = 1X,X be the sample covariance matrix. Let λι > λ2 > . . . > λ, be the ordered eigenvalues of S. Let el, . . . , ep be their corresponding orthogonal eigenvectors with unit length. In multivariate analysis, we usually want to use the first few eigenvalues and eigenvectors to represent the original data, as a tool...
Let X1 be a normal random variable with mean 2 and variance 3, and let X2 be a normal random variable with mean 1 and variance 4. Assume that X1 and X2 are independent. What is the distribution of the linear combination Y = 2X1 + 3X2?
= = 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...
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 =...
9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c) Sn=X1+X2 + . . . + Xn. (d) An -Sn/n 9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c)...
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...
MULTIVARIATE DISTRIBUTIONS 3. Suppose that Xi and X2 are independent and each has a uniform distribution on (0,1). Define Y: X1 + X2 and Y2 = X1-X2. Find the marginal probability density functions of Y1 and Y2. . Suppose that X has a standard normal distribution, and that the conditional distribution of Y given X is a normal distribution with mean 2X 3 and variance 12. Find E(Y) and Var(Y)