A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Transcribed Image Text:Q2. 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
Transcribed Image Text:(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? IHow 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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