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

Question

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 arc the pairwise correlations between the different counts (n_i, ' s)?

Explanation / Answer

a)

required probability = 0.4 * 0.4 * 0.4 * 0.4 * 0.2*0.2 = 0.001024

b)

required probability = 1 - no stock has positive return

= 1 - 0.6 * 0.6 *0.6*06 *0.6 * 0.6

= 0.953344

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