Two safety inspectors inspect a new building and assign it a safety score of 1, 2,...

 

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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 0.09 0.02 0.2 0.02 2 0.01 0.1 0.1 0.03 0.04 0.01 0.04 0.01 0.02 (a) What is the probability that both inspectors assign different safety 0.2 4 0.1 0.01 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 0.09 0.02 0.2 0.02 2 0.01 0.1 0.1 0.03 0.04 0.01 0.04 0.01 0.02 (a) What is the probability that both inspectors assign different safety 0.2 4 0.1 0.01 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?