Q 6.3. Let X = (X₁, X2,..., Xn)T be a random vector with mean vector µ and variance-covariance matrix E. Suppose that for every a =(a1, a2,...,,an)TE R¹, the random variablea X has a (one-dimensional) Gaussian distribution on R.(a) For fixed a € R", compute the moment generating function Marx(u) of the randomvariable a X writing the answer using and Σ.(b) Define Mx (t₁, t2, ..., tn), the moment generating function of the random vector X, and ex-press it in terms of Mtrx the moment generating function of t¹ X where t=(t₁, t2,. , tn).Combining (a) and (b), compute the moment generating function Mx (t) of X and henceprove that the random vector X has a Gaussian distribution.

Given that be a random vector with mean vector and variance-covariance matrix .

Answered: Q 6.3. Let X = (X1, X2,..., Xn) be a…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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