1. Given that the density function of a p × 1 normal random vector x isƒ(x) = (2n)−³ | 27 |¯‡ exp{-} (x − µ)²x−¹(x − µ}},show that the m.g.f. of a is{ t²u₁ + } t³²_t } ₁Mr(t) = E{exp(t²x)} = expx = R¹,t ERP.1/2t. You canHint: Make a linear transformation to y = -1/2(x-μ), and set s =use the fact that if z ~ N₁(0, 1) is a univariate random variable with a standard normaldistribution, then its m.g.f. is M₂(t) = exp(t²/2).

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Answered: 1. Given that the density function of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. Given that the density function of a p × 1 normal random vector a is ƒ(x) = (2π)−² | C |¯½ exp 1/(x − μµ)² (¯`-¹²(x − µ)}]}, - show that the m.g.f. of x is M₂(t) = E{exp(t¹x)} = exp· μ+ [txt}, x ERP. t ERP.