A certain financial theory posits that daily fluctuations in stock prices are independent random variables. Suppose that the daily price fluctuations (in dollars) of a certain value stock are independent and identically distributed random variables X1, X2, X3,..., with EXi = 0.01 and Var Xi = 0.01. (Thus, if todayâs price of this stock is $50, then tomorrowâs price is $50 + X1, etc.) Suppose that the daily price fluctuations (in dollars) of a certain growth stock are independent and identically distributed random variables Y1, Y2, Y3,..., with EYj = 0 and Var Yj = 0.25. Now suppose that both stocks are currently selling for $50 per share and you wish to invest $50 in one of these two stocks for a period of 400 market days. Assume that the costs of purchasing and selling a share of either stock are zero.
(a) Approximate the probability that you will make a profit on your investment if you purchase a share of the value stock.
(b) Approximate the probability that you will make a profit on your investment if you purchase a share of the growth stock.
(c) Approximate the probability that you will make a profit of at least $20 if you purchase a share of the value stock.
(d) Approximate the probability that you will make a profit of at least $20 if you purchase a share of the growth stock.
(e) Assuming that the growth stock fluctuations and the value stock fluctuations are independent, approximate the probability that,