2. You are thinking of investing $100,000 in the biotechnology business. There are two companies in which you can invest: Astutebio (A) and Biosmart (B). If you invest in one of these companies and it succeeds to develop a drug and obtain FDA approval then you will quadruple your money. If it does not succeed, then you will lose your money. The probability of success if each firm is ) and the success or failure of each firm is unrelated to what happens in the other. a) For each of the following scenarios, describe (1) the payoff that you obtain in each possible case, the corresponding rate of return and the associated probability; (2) the expected value; and (3) the standard deviation of the rate of return of your investment i. You invest everything in A ii. You invest in A and % in B iii You invest in A and % in B IV. You invest 1/3 in A and 2/3 in B You invest all in B b) Check that in the five scenarios of question (a) the standard deviation that you found is oo+pio 2. You are thinking of investing $100,000 in the biotechnology business. There are two companies in which you can invest: Astutebio (A) and Biosmart (B). If you invest in one of these companies and it succeeds to develop a drug and obtain FDA approval then you will quadruple your money. If it does not succeed, then you will lose your money. The probability of success if each firm is ) and the success or failure of each firm is unrelated to what happens in the other. a) For each of the following scenarios, describe (1) the payoff that you obtain in each possible case, the corresponding rate of return and the associated probability; (2) the expected value; and (3) the standard deviation of the rate of return of your investment i. You invest everything in A ii. You invest in A and % in B iii You invest in A and % in B IV. You invest 1/3 in A and 2/3 in B You invest all in B b) Check that in the five scenarios of question (a) the standard deviation that you found is oo+pio