" Probability And Statistics for Engineers And Scientists, Hayter, A. (2007), Chapter 2 1 1. 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. X 1 2 3 4 0.09 0.03 0.01 0.01 Y 2 0.02 0.15 0.03 0.01 3 0.01 0.01 0.24 0.04 4 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