(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?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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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.
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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? 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?
Transcribed Image Text: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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