Suppose that a person invests in 6 stocks, each with a 40% chance of havingno return, a 30% chance of having a positive return, and a 30% chance of havinga negative return. you may assume that the stocks are independent and the probabilities do not change. let(n1; n2; n3)be the number of stocks with noreturns, positive returns and negative returns respectively.

(a) find the probability that 2 stocks have no return, 2 have positive returns, and 2 have negative returns.
(b) find the probability that at least one stock has a positive return.
(c) find the expected values and standard deviations of n 1; n2 n3.
(d) find the pairwise correlations ofn1; n2; n3.