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In Exercise 5.6, we assumed that if a radioactive particle is randomly located in a square with sides of unit length, a reasonable model for the joint density function for Y1 and Y2 is f(V1. y2) = | 1, 0sy < 1,0< y < 1, 10, elsewhere. a Find the marginal density functions for Y, and Y2. b What is P(.3 < Y1 < .5)? P(.3 < Y2 < .5)? c For what values of y, is the conditional density f(yıly2) defined?

In Exercise 5.6, we assumed that if a radioactive particle is randomly located in a square with sides of unit length, a reasonable model for the joint density function for Y1 and Y2 is f(V1. y2) = | 1, 0sy < 1,0< y < 1, 10, elsewhere. a Find the marginal density functions for Y, and Y2. b What is P(.3 < Y1 < .5)? P(.3 < Y2 < .5)? c For what values of y, is the conditional density f(yıly2) defined?

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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In Exercise 5.6, we assumed that if a radioactive particle is randomly located in a square with sides of unit length, a reasonable model for the joint density function for Y1 and Y2 is f(1. Y2) =0, clsewhere. | 1, 0<y < 1,0 < y2 < 1, a Find the marginal density functions for Y1 and Y2. b What is P(.3 < Yı < .5)? P(.3 < Y, < 5)? c For what values of yz is the conditional density f(yıly2) defined? d For any y2, 0 < 2 <1 what is the conditional density function of Y, given that Y, = y2? e Find P(.3 < Y, < .5|Y2 = .3). f Find P(.3 < Y, < .5|Y2 = .5). g Compare the answers that you obtained in parts (a), (d), and (e). For any y2, 0 < y < 1 how does P(.3 < Y, < .5) compare to P(.3 < Y1 < .5|Y2 = y2)?
Transcribed Image Text:In Exercise 5.6, we assumed that if a radioactive particle is randomly located in a square with sides of unit length, a reasonable model for the joint density function for Y1 and Y2 is f(1. Y2) =0, clsewhere. | 1, 0<y < 1,0 < y2 < 1, a Find the marginal density functions for Y1 and Y2. b What is P(.3 < Yı < .5)? P(.3 < Y, < 5)? c For what values of yz is the conditional density f(yıly2) defined? d For any y2, 0 < 2 <1 what is the conditional density function of Y, given that Y, = y2? e Find P(.3 < Y, < .5|Y2 = .3). f Find P(.3 < Y, < .5|Y2 = .5). g Compare the answers that you obtained in parts (a), (d), and (e). For any y2, 0 < y < 1 how does P(.3 < Y, < .5) compare to P(.3 < Y1 < .5|Y2 = y2)?
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