solve step by step.

problem(2)

Question I want answered:

(12 points) Batman and Robin have decided to have a criminal catching competition. Let B denote the number of criminals caught by Batman and let R denote the number of criminals caught by Robin. Suppose that the joint pmf of B and R is given by the following table: R 0 1 2 3 0.08 .07 .04 .00 1 .06 .10 .02 .04 B 2.05 .04 .10 .06 3.05 .03 .04 .07 4.03 .01 .05 .06 (a) What are the marginal pmfs for Batman and Robin? (2 points) (b) What is the covariance between the number of criminals caught by Batman and the number caught by Robin? (4 points) (c) What is the correlation between the number of criminals caught by Batman and the number caught by Robin? (4 points) (d) What is the strength of the relationship between the number of criminals caught by Batman and the number caught by Robin? How do you know? (2 points) 8 points) Return to the scenario described in question 2. Suppose Commissioner Gor- on, Batman's police contact and friend, has decided to incentivize the Dynamic Duo, by warding them a monetary bonus for each criminal they capture funded through city taxes. uppose Gordon will pay Batman $100 for every criminal he catches and Robin $150 for Every criminal he catches. (a) Establish a function that will track the amount of money that the city will have to pay to the caped crusaders. (2 points) (b) How much money should the city expect to pay at the end of the night? (6 points)