A random point (X, Y) is uniformly distributed on the 2 x 2 square ith vertices at (1, 1), (–1, 1), (1, –1), (–1, –1). That is, the joint pdf is inverse of the total rea, f(x,y) = 1/4 with support on the square. Determine the following probabilities. 1. P(X² +Y² < 1). 2. P(2X – Y > 0). 3. P(|X +Y|< 2). lint: think geometrically and express the regions you are integrating over as regular geo- notuio ahoneg for which
A random point (X, Y) is uniformly distributed on the 2 x 2 square ith vertices at (1, 1), (–1, 1), (1, –1), (–1, –1). That is, the joint pdf is inverse of the total rea, f(x,y) = 1/4 with support on the square. Determine the following probabilities. 1. P(X² +Y² < 1). 2. P(2X – Y > 0). 3. P(|X +Y|< 2). lint: think geometrically and express the regions you are integrating over as regular geo- notuio ahoneg for which
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Answer parts 1, 2, and 3 of the question. Show all work/steps.

Transcribed Image Text:A random point (X,Y) is uniformly distributed on the 2 x 2 square
with vertices at (1,1), (–1, 1), (1, –1), (–1, –1). That is, the joint pdf is inverse of the total
area, f(x, y) = 1/4 with support on the square. Determine the following probabilities.
1.
P(X² + Y² < 1).
2.
P(2X – Y > 0).
3.
P(|X +Y| < 2).
Hint: think geometrically and express the regions you are integrating over as regular geo-
metric shapes for which you can compute areas.
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