Exercise 3: Suppose that in an electric display sign there are three light bulbs in the first row and four light bulbs in the second row. Let X denote the mumber of bulbs in the first row that will be burned out at a specified time t, and let Y denote the mumber of bulbs in the second row that will be burned out at the same time t. Suppose that the joint p.f of X and Y is as specified in the following table: 1. 3 0.08 0.07 0.06 0.01 0.01 1 0.06 0.10 0.12 0.05 0.02 2 0.05 0.06 0.09 0.04 0.03 3 0.02 0.03 0.03 0.03 0.04 Determine cach of the following probabilities: 1. Pr(X = 2) 2. Pr(Y > 2) 3. Pr(Y < 2|X = 3) and Var[Y|Y = 3], Var[Y|X = 3]
Exercise 3: Suppose that in an electric display sign there are three light bulbs in the first row and four light bulbs in the second row. Let X denote the mumber of bulbs in the first row that will be burned out at a specified time t, and let Y denote the mumber of bulbs in the second row that will be burned out at the same time t. Suppose that the joint p.f of X and Y is as specified in the following table: 1. 3 0.08 0.07 0.06 0.01 0.01 1 0.06 0.10 0.12 0.05 0.02 2 0.05 0.06 0.09 0.04 0.03 3 0.02 0.03 0.03 0.03 0.04 Determine cach of the following probabilities: 1. Pr(X = 2) 2. Pr(Y > 2) 3. Pr(Y < 2|X = 3) and Var[Y|Y = 3], Var[Y|X = 3]
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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Question
part 3
![Exercise 3: Suppose that in an electric display sign there are three light bulbs
in the first row and four light bulbs in the second row. Let X denote the mumber
of bulbs in the first row that will be burned out at a specified time t, and let Y
denote the number of bulbs in the second row that will be burned out at the same
time t. Suppose that the joint p.f of X and Y is as specified in the following table:
2
3
4
0.08 0.07 0.06 0.01 0.01
1
0.06 0.10 0.12 0.05 0.02
2
0.05 0.06 0.09
0.04
0.03
3
0.02 0.03 0.03 0.03 0.04
Determine each of the following probabilities:
1. Pr(X = 2)
2. Pr(Y > 2)
3. Pr(Y < 2|X = 3) and Var[Y|Y = 3], Var[Y|X = 3]
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb82d15e0-7327-49cc-b0aa-5e3627d09d5f%2F23d09960-0a7f-41fc-9578-19cf92116275%2Fk4kfs7h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 3: Suppose that in an electric display sign there are three light bulbs
in the first row and four light bulbs in the second row. Let X denote the mumber
of bulbs in the first row that will be burned out at a specified time t, and let Y
denote the number of bulbs in the second row that will be burned out at the same
time t. Suppose that the joint p.f of X and Y is as specified in the following table:
2
3
4
0.08 0.07 0.06 0.01 0.01
1
0.06 0.10 0.12 0.05 0.02
2
0.05 0.06 0.09
0.04
0.03
3
0.02 0.03 0.03 0.03 0.04
Determine each of the following probabilities:
1. Pr(X = 2)
2. Pr(Y > 2)
3. Pr(Y < 2|X = 3) and Var[Y|Y = 3], Var[Y|X = 3]
%3D
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