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2. ( region R in the plane if, for some constant c, its joint density is ) The random vector (X, Y) is said to be uniformly distributed over a 1/5 c, if (x, y) E R f(x, y) = { 0, otherwise. (a) Show that 1/c= area of region R. Suppose that (X,Y) is uniformly distributed over the square centered at (0,0), whose sides are of length 2. (b) Show that X and Y are independent, with each being distributed uniformly over (-1, 1). (c) What is the probability that (X, Y) lies in the circle of radius 1 centered at the origin? That is, find Prob(X² +Y² < 1).

2. ( region R in the plane if, for some constant c, its joint density is ) The random vector (X, Y) is said to be uniformly distributed over a 1/5 c, if (x, y) E R f(x, y) = { 0, otherwise. (a) Show that 1/c= area of region R. Suppose that (X,Y) is uniformly distributed over the square centered at (0,0), whose sides are of length 2. (b) Show that X and Y are independent, with each being distributed uniformly over (-1, 1). (c) What is the probability that (X, Y) lies in the circle of radius 1 centered at the origin? That is, find Prob(X² +Y² < 1).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. ( :) The random vector (X, Y) is said to be uniformly distributed over a region R in the plane if, for some constant c, its joint density is 1/5 { Įc, if (x, y) ER f(x, y) 0, otherwise. (a) Show that 1/c = area of region R. Suppose that (X,Y) is uniformly distributed over the square centered at (0,0), whose sides are of length 2. (b) Show that X and Y are independent, with each being distributed uniformly over (-1, 1). (c) What at the origin? That is, find Prob(X² + Y² < 1). the probability that (X, Y) lies in the circle of radius 1 centered :::
Transcribed Image Text:2. ( :) The random vector (X, Y) is said to be uniformly distributed over a region R in the plane if, for some constant c, its joint density is 1/5 { Įc, if (x, y) ER f(x, y) 0, otherwise. (a) Show that 1/c = area of region R. Suppose that (X,Y) is uniformly distributed over the square centered at (0,0), whose sides are of length 2. (b) Show that X and Y are independent, with each being distributed uniformly over (-1, 1). (c) What at the origin? That is, find Prob(X² + Y² < 1). the probability that (X, Y) lies in the circle of radius 1 centered :::
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