A 2 × 1 random vector is given by Answer the following questions: (a) Let X,-íj

Question

A 2 × 1 random vector is given by Answer the following questions: (a) Let X,-íj and X2-SU where var( )-1. Find the covariance matrix of the resulting X in in equation (1). You can denote the matrix by any capital letter you chose. (b) For the same X1 = U and X2 = 3U as in problem (2a), find the correlation (c) Is the covariance matrix of X computed above in problem (2b) positive definite? (d) Now consider arbitrary Xi and X2 as in equation (1). i.e., the entries of X are coefficient px1,X2 Explain why or why not not limited to those given in problem (2a). Under what conditions on Xi and X;2 is the var(X1 + X2) -var(X1) without X2 being a constant? (e) If Xi and X2 are jointly Gaussian with the joint PDF find the joint PDF of the transformed random vector 2

Explanation / Answer

the covariance matrix of the resulting equation is A=[1

3] IS THE covariance matrix of the system

b.the correlation function of the random 2×1 vector is in the range of -1 to +1

c.the covariance matrix of the value is computed is a positive value because the correlated function contains the eigen vector values which are been transformed into the probability denstiy function

d.under the condition x1+x2 =var x1 without x2 in this function the mean value of the matrix vector is been calculated and the functions are plotted with the eigen values of a matrix from guassian distribution of the system

e.the joint pdf function of the given matrix is the no of distribution of the function based on the bernoulis equation and the joint pdf of the function is 2/9

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