Example 6-21. Let X1, X2, ... , X, be a sequence of mutually independent randomvariables with common distribution. Suppose Xk assumes only positive integral values and E.(Xx) = a exists ; k = 1, 2, ..., n. Let S„ = X1 + X2 +... + X -+ X, .%3Dm(i) Show that ESfor 1 Sm Sn%3D

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Answered: Example 6-21. Let X1, X2, ... , X, be 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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Q 6.1. Suppose Z = (Z1, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., for i ≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)-(d), on the left is equal in distribution to exactly one random variables, (1)-(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. (a) (X₂) (¹) (X) = (2) 1/√2 (Ⓒ) (x₂) - (3/1² ¹1/1²) (2) (c = 2 0 = 2 Z₁ 1) (²) 3 (4¹) (X) = (²¹) (1) (2) (3) Y₁ 1 (29) - ()) (2) = Y₂ 1 Y₁ (121) = (1/² √₂) (2) (1/√2 1/√2 /2 −1/√√2, Y₂ X₁ X₂ = 22 1 1 2 0 Y₁ 2 1 (4) (2)) = (²) (²) 1 1 Z₁ Z₂ Z3
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Example 6-21. Let X1, X2, ... , X, be a sequence of mutually independent random variables with common distribution. Suppose Xg assumes only positive integral values and E (Xp) = a exists; k = 1, 2, . ..., n. Let S, = X1 + X2 + + X, . %3D %3D %3D ... m (i) Show that E for 1 Sm Sn