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- 6. Show that if E|X₁|' < ∞, j ≥ 2, then E|X₁ − µ|¹ ≤ 2¹ E|X₁|³. Hint: By the iterated expectation theorem - E|X₁ − µ|¹ = E{|X₁ − µ|³ ||X₁| ≥ |µ|}P(|X₁| ≥ |µ|) +E{|X₁ − µ|³ ||X₁| < |µ|}P(|X₁| < |µ|).

- 6. Show that if E|X₁|' < ∞, j ≥ 2, then E|X₁ − µ|¹ ≤ 2¹ E|X₁|³. Hint: By the iterated expectation theorem - E|X₁ − µ|¹ = E{|X₁ − µ|³ ||X₁| ≥ |µ|}P(|X₁| ≥ |µ|) +E{|X₁ − µ|³ ||X₁| < |µ|}P(|X₁| < |µ|).

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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6. Show that if E|X₁| <∞, j≥ 2, then E|X₁ - μ³ ≤2¹E|X₁|³. Hint: By the iterated expectation theorem E|X₁ − µ|¹ = E{|X1 − µ|¹ ||X₁| ≥ |µ|}P(|X1| ≥ |M|) +E{|X₁ − μ|³||X₁| < |µ|}P(|X₁| < |µ).
Transcribed Image Text:6. Show that if E|X₁| <∞, j≥ 2, then E|X₁ - μ³ ≤2¹E|X₁|³. Hint: By the iterated expectation theorem E|X₁ − µ|¹ = E{|X1 − µ|¹ ||X₁| ≥ |µ|}P(|X1| ≥ |M|) +E{|X₁ − μ|³||X₁| < |µ|}P(|X₁| < |µ).
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