Homework Help is Here – Start Your Trial Now!
Math
Statistics
Check that the standard normal PDF p(x)=e-r²/v2™ satisfies the equation I xp(x)dx = p(y). y>0. By using this equation and sin x= ,' cos ydy, or otherwise, prove that if X is an N(0, 1) random variable, then (Ecos X) < Var (sin X) < E(cos X).

Check that the standard normal PDF p(x)=e-r²/v2™ satisfies the equation I xp(x)dx = p(y). y>0. By using this equation and sin x= ,' cos ydy, or otherwise, prove that if X is an N(0, 1) random variable, then (Ecos X) < Var (sin X) < E(cos X).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 18E
See similar textbooks
icon
Related questions
Question
Check that the standard normal PDF p(x) =e-12//2# satisfies the equation | xp(x)dx = p(y). y> 0. By using this equation and sin.x= [, cos ydy, or otherwise, prove that if X is an N(0, 1) random variable, then (E cos X) < Var (sin X) < E(cos X)².
Transcribed Image Text:Check that the standard normal PDF p(x) =e-12//2# satisfies the equation | xp(x)dx = p(y). y> 0. By using this equation and sin.x= [, cos ydy, or otherwise, prove that if X is an N(0, 1) random variable, then (E cos X) < Var (sin X) < E(cos X)².
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer