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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.4: Complex Numbers

Problem 59E

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Let random variables X₁ and X₂ be uncorrelated and each
distributed according to
2x
fx(x) = {
0 ≤ x ≤T,
otherwise
a) Find the nth moment of X; about the origin.
b) Let Y
=
3X₁ + X₂. Find the second moment about the origin of Y, then find its
variance.
c) Let Z
=
aX₁ + 6X₂, and W = aX₁ — bX2. Determine the condition on a and b such
that Z and W are uncorrelated.
d) When the condition you found is satisfied, are W and Z also independent? Justify
fully.

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