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● Show Y~ N(0, 1). Hint: Find the P[Y

● Show Y~ N(0, 1). Hint: Find the P[Y

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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1. Show for RVs (X, Y), independence results in px,y = 0. 2. For jointly Gaussian RVs, show px,y = 0 results in independence. 3. Let X~ N(0, 1). Let Y = 1 with probability and Y = -X with probability (e.g., depending on throw of a coin head or tail, we get Y = X or Y = -X). Show Y~ N(0, 1). Hint: Find the CDF of Y and note that P[Y <a] = P[Y <a/A] P[A] + P[Y <a Aº] P[A] . Show px, y = 0 Show that X, Y are not independent. • Find joint probability distribution of X, Y (simplify as much as you can). Moral of the story: If two normal RVs are not jointly Gaussian, p = 0 does not lead to independence.
Transcribed Image Text:1. Show for RVs (X, Y), independence results in px,y = 0. 2. For jointly Gaussian RVs, show px,y = 0 results in independence. 3. Let X~ N(0, 1). Let Y = 1 with probability and Y = -X with probability (e.g., depending on throw of a coin head or tail, we get Y = X or Y = -X). Show Y~ N(0, 1). Hint: Find the CDF of Y and note that P[Y <a] = P[Y <a/A] P[A] + P[Y <a Aº] P[A] . Show px, y = 0 Show that X, Y are not independent. • Find joint probability distribution of X, Y (simplify as much as you can). Moral of the story: If two normal RVs are not jointly Gaussian, p = 0 does not lead to independence.
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