Question

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 Figure below.

(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? Would you expect them to be

independent? How would you interpret the situation if they were independent?

(f) If the first inspector assigns a score of 3, what is the conditional probability mass function of the score

assigned by the second inspector?

(g) What is the covariance of the scores assigned by the two inspectors?

(h) 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?​

Answer 1

Answer:

Step-by-step explanation:

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