Suppose that a person invests in 6 stocks, each of which has a 40% of having no return, a 40% chance of having

a positive return, and a 20% chance of having a negative return. You may assume the stocks are independent, and the probabilities do not change.

(a) Find the probability that 2 stocks have no return, 2 have a negative return, and 2 have a positive return.

(b) Find the probability that at least one stock has a positive return.

(c) Find the expected value for each outcome, and the standard deviation.

(d) What are the pairwise correlations between the different counts (n_i's)?