(a) What is the probability that both inspectors assign different safety score? (b) What is the probability that the first inspector assigns a higher safety score than the second inspector? (c) Are the scores assigned by the two inspectors independent of each other? Would you expect them to be independent? How would you interpret the situation if they were independent? (d) If the first inspector assigns a score of 2, what is the conditional variance of the score assigned by the second inspector? (e) What is the correlation between the scores assigned by the two inspectors? If you are responsible for training the safety inspectors to perform proper safety evaluations of buildings, what correlation value would you like there to be between the scores of two safety inspectors?

(a) What is the probability that both inspectors assign different safety score? (b) What is the probability that the first inspector assigns a higher safety score than the second inspector? (c) Are the scores assigned by the two inspectors independent of each other? Would you expect them to be independent? How would you interpret the situation if they were independent? (d) If the first inspector assigns a score of 2, what is the conditional variance of the score assigned by the second inspector? (e) What is the correlation between the scores assigned by the two inspectors? If you are responsible for training the safety inspectors to perform proper safety evaluations of buildings, what correlation value would you like there to be between the scores of two safety inspectors?

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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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

(a) What is the probability that both inspectors assign different safety
score?
(b) What is the probability that the first inspector assigns a higher
safety score than the second inspector?
(c) Are the scores assigned by the two inspectors independent of each
other? Would you expect them to be independent? How would
you interpret the situation if they were independent?
(d) If the first inspector assigns a score of 2, what is the conditional
variance of the score assigned by the second inspector?
(e) What is the correlation between the scores assigned by the two
inspectors? If you are responsible for training the safety inspectors
to perform proper safety evaluations of buildings, what correlation
value would you like there to be between the scores of two safety
inspectors?

Two safety inspectors inspect a new building and assign it a “safety
score" of 1, 2, 3, or 4. Suppose that the random variable X is the score
assigned by the first inspector and the random variable Y is the score
assigned by the second inspector, and that they have a joint probability
mass function given in the following table:
Y
1
2
3
4
1
0.09
0.02
0.2
0.02
2
0.01
0.1
0.1
0.03
3
0.04
0.01
0.04
0.2
4
0.01
0.02
0.1
0.01

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