(12 points) The random variables X1, X2, and X; are jointly Gaussian with the following mean...
Can someone please help solve the problem below? I keep getting the answer incorrect. = (12 points) The random variables X1, X2, and X3 are jointly Gaussian with the following mean vector and covariance matrix: [4 2 0 = 2 5 -1 0-1 The random variable Y is formed from X1, X2, and X; as follows: Y=X1 - X2 + X: +4. Determine P(Y> 3). X x 3 1
Can someone please help solve the problem below? I keep getting the answer incorrect. = (12 points) The random variables X1, X2, and X3 are jointly Gaussian with the following mean vector and covariance matrix: [4 2 0 = 2 5 -1 0-1 The random variable Y is formed from X1, X2, and X; as follows: Y=X1 - X2 + X: +4. Determine P(Y> 3). X x 3 1
Can someone please help solve the problem below? I keep getting the answer incorrect. = (12 points) The random variables X1, X2, and X3 are jointly Gaussian with the following mean vector and covariance matrix: [4 2 0 = 2 5 -1 0-1 The random variable Y is formed from X1, X2, and X; as follows: Y=X1 - X2 + X: +4. Determine P(Y> 3). X x 3 1
3 -0.751 (X1,X2, X3) be jointly Gaussian with ux (1,-2,3) and Cx 1. Let X = 3 0.25 4 L-0.75 0.25 Hint: If a set of random variables (RVs) are jointly Gaussian, then any subset of those RVs are also jointly Gaussian. Similarly, adding constants to (or taking linear combinations of) jointly Gaussian RVs results in jointly Gaussian RVs. Using this property you can solve problem 1 without using integration. When appropriate, you may express your answer by saying that...
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
number2 how to solve it? Are x1 and x2 independent - yes, they are independent. Random variables X and Y having the joint density 1. 8 2)u(y 1)xy2 exp(4 2xy) fxy (x, y) ux- _ 3 1 1 Undergo a transformation T: 1 to generate new random variables Y -1. and Y2. Find the joint density of Y and Y2 X3)1/2 when X1 and X2 (XR 2. Determine the density of Y are joint Gaussian random variables with zero means...
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...
2. (30 Points) X and Y ~ N (0,4) are two jointly Gaussian random variables, and E(XY) = 3 a. (10 Points) Find their joint PDF, f (x,y). b. (10 Points) Find the mean and variance of Z = X +Y. c. (10 Points) Find the mean and variance of Z = X + Y + 2.
1. (20 points) Let X (Xi, X, Xs) be a real random vector, where X, are identically dis- tributed and independent (ii.d.) zero-mean Gaussian real random variables. Consider the random vector Y given by where A is a 3 x 3 real matrix and b is a 3 x 1 real vector. Justify all your answers. (a) Find the covariance matrix Cx of x. (b) Find the mean vector EY] of Y (c) Express the covariance matrix Cy of Y...
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in order to compute the sum x3=x1+x2. We want to prove that: a) x3 follows a gaussian distribution b) estimate mean value μ3 and variance σ3^2 c) repeat the above steps for multivariate Gaussian distributions N1~(μ1,Σ1) and N2~(μ2,Σ2)