A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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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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Transcribed Image Text: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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