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44. If X-N (0, 1) and Y-N (0, 1), prove that (1) Var (sin X) > Var (cos X) (ii) EIX-YIS √8/T

44. If X-N (0, 1) and Y-N (0, 1), prove that (1) Var (sin X) > Var (cos X) (ii) EIX-YIS √8/T

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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The image shows the following mathematical expression and problem statement for an educational exercise: **Problem 44**: If \( X \sim \mathcal{N}(0, 1) \) and \( Y \sim \mathcal{N}(0, 1) \), prove that: (i) \( \text{Var}(\sin X) > \text{Var}(\cos X) \). (ii) \( E|X - Y| \leq \sqrt{\frac{8}{\pi}} \). This problem involves proving inequalities related to the variances and expected values of normally distributed random variables and their trigonometric transformations.
Transcribed Image Text:The image shows the following mathematical expression and problem statement for an educational exercise: **Problem 44**: If \( X \sim \mathcal{N}(0, 1) \) and \( Y \sim \mathcal{N}(0, 1) \), prove that: (i) \( \text{Var}(\sin X) > \text{Var}(\cos X) \). (ii) \( E|X - Y| \leq \sqrt{\frac{8}{\pi}} \). This problem involves proving inequalities related to the variances and expected values of normally distributed random variables and their trigonometric transformations.
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