1. A financial advisor interviewed their clients to determine the number of credit cards that they own, along with their owed credit card debt rounded to the nearest thousand dollars. Let X be the number of credit cards that a client owns and Y the credit card debt owed by the client (measured in thousands of dollars). The results of these interviews are summarized in the table below. Y 0 1 2 3 4 5 1 0.04 0.05 0.1 0.07 0.03 0.01 X 2 0.02 0.15 0.12 0.11 0.06 0.05 3 0.01 0.01 0.02 0.04 0.04 0.07 (a) Find the marginal distributions for X and Y. (b) Determine the expected value of Y, i.e., the expected amount of credit card debt that a client owes. (c) Find the conditional distribution for X, the number of credit cards that a client owns, given that they owe $3,000 in credit card debt.