The Troubled Asset Relief Program (TARP), passed by the U.S. Congress in October 2008, provided $700 billion in assistance for the struggling U.S. economy. Over $200 billion was given to troubled financial institutions with the hope that there would be an increase in lending to help jump-start the economy. But three months later, a Federal Reserve survey found that two-thirds of the banks that had received TARP funds had tightened terms for business loans (The Wall Street Journal, February 3, 2009). Of the ten banks that were the biggest recipients of TARP funds, only three had actually increased lending during this period.

For the purposes of this exercise, assume that you will randomly select three of these ten banks for a study that will continue to monitor bank lending practices. Let x be a random variable indicating the number of banks in the study that had increased lending.

a. What is f(0)? What is your interpretation of this value?

b. What is f(3)? What is your interpretation of this value?

c. Compute f(1) and f(2). Show the probability distribution for the number of banks in the study that had increased lending. What value of x has the highest probability?

d. What is the probability that the study will have at least one bank that had increased lending?

e. Compute the expected value, variance, and standard deviation for the random variable.