(Solved): 7. A bivariate probability mass function is given below for the random variables \( X \) and \( Y ...

7. A bivariate probability mass function is given below for the random variables \( X \) and \( Y \) related to whether car tires are underinflated and whether the tires are worn unevenly or not. \( X=0 \) if no tires are underinflated, \( X=1 \) if exactly one tire is underinflated, and \( X=2 \) if two or more tires are underinflated. \( Y=0 \) if no tires are worn unevenly and \( Y=1 \) if at least one tire is worn unevenly. (a) What is the conditional probability distribution for \( Y \) given that \( X=1 \) ? (List the possible values and their probabilities.) (b) What is the covariance of \( X \) and \( Y \) ? Use the fact that \( E(X)=1.3 \) and \( E(Y)=.7 \).