(15 pts) Determine whether the statement is true or false. Explain your reasoning in detail. (a) (3 pts) If there are two events (A and B), P(B|A)=P(A|B) is irnposible. (b) (3 pts) Suppose that, in a small town of 50 people, one person earns $5,000,000 per year and the other 49 each earn $30,000. Median is better measurement to explore the income inequality in the small town. (c) (3 pts) If the two events are mutually exclusive, P(A and B)=P(A)*P(B). (d) (3 pts) X and Y are random variables. We have Cov(aX+b, cY+d)=acCov(X, Y), where a, b, c, and d are constants. (e) (3 pts) The number of dogs (X) per household in a. small town. The table shows a discrete distribution of X lnTlol-l'zlslzysl ' Probability ' 0.686 i 0.195 0.077 ' 0.022 ' 0.013 0.007