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1. let X be a real random variable having moments of any order, such that (2k) k Show that the support of X is included in [-2, 2] Vk > 0, m2k (X) = et m2k+1(X) = 0

1. let X be a real random variable having moments of any order, such that (2k) k Show that the support of X is included in [-2, 2] Vk > 0, m2k (X) = et m2k+1(X) = 0

MATLAB: An Introduction with Applications
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. let X be a real random variable having moments of any order, such that (*) 2k Vk> 0, тк(X) — et m2k+1(X) = 0 k Show that the support of X is included in [-2, 2] Let 0 be a random variable with uniform distribution over [-T, T]. We set Y = 2cose 2. Determine the moments of Y. Deduce that X and Y are equal in law. 3. Show that the law of Y admits a density that we will calculate 4. Determine the distribution function of the law of Y 5 Determine the law of Z = Y² et de U = . 2+Y et means (and ) de means (of) ww
Transcribed Image Text:1. let X be a real random variable having moments of any order, such that (*) 2k Vk> 0, тк(X) — et m2k+1(X) = 0 k Show that the support of X is included in [-2, 2] Let 0 be a random variable with uniform distribution over [-T, T]. We set Y = 2cose 2. Determine the moments of Y. Deduce that X and Y are equal in law. 3. Show that the law of Y admits a density that we will calculate 4. Determine the distribution function of the law of Y 5 Determine the law of Z = Y² et de U = . 2+Y et means (and ) de means (of) ww
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