Please solve b, d, and f parts. . a Two safety inspectors inspect a new building and assign it a "safety score" of 1,2,3, or 4. Supposethat the random variable X is the score assigned by the first inspector and the random variable Y is thescore assigned by the second inspector, and they have a joint probability mass function given below.1Y 234X123 40.09 0.030.010.010.15 0.03 0.010.020.01 0.01 0.24 0.040.00 0.01 0.02 0.32(a) What is the probability that both inspectors assign the same safety score?(b) What is the probability that the second inspector assigns a higher safety score than the firstinspector?(c) What are the marginal probability mass function, expectation, and variance of the score assignedby the first inspector?(d) What are the marginal probability mass function, expectation, and variance of the score assignedby the second inspector?(e) Are the scores assigned by the two inspectors independent of each other?(f) What are the covariance of the scores assigned by the two inspectors?

Answered: Image /qna-images/answer/2342ca4c-6587-44f3-9c9c-0112853ec720.jpg

Answered: Please solve b, d, and f parts.

Math

Statistics

Please solve b, d, and f parts.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 85E

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Question

Please solve b, d, and f parts.

. a 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 they have a joint probability mass function given below.
1
Y 2
3
4
X
1
2
3 4
0.09 0.03
0.01
0.01
0.15 0.03 0.01
0.02
0.01 0.01 0.24 0.04
0.00 0.01 0.02 0.32
(a) What is the probability that both inspectors assign the same safety score?
(b) What is the probability that the second inspector assigns a higher safety score than the first
inspector?
(c) What are the marginal probability mass function, expectation, and variance of the score assigned
by the first inspector?
(d) What are the marginal probability mass function, expectation, and variance of the score assigned
by the second inspector?
(e) Are the scores assigned by the two inspectors independent of each other?
(f) What are the covariance of the scores assigned by the two inspectors?

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