A share of common stock in the Pilsdorff beer company has a price Yn on the nth business day of the year. Finn observes that the price change Xn = Yn+1 - Yn appears to be a random variable with mean µ = 0 and variance σ2 = 1/4. If Y1 = 30, find a lower bound for the following probabilities, under the assumption that the Xn's are mutually independent.
(a) P (25 ≤ Y2 ≤ 35).
(b) P (25 ≤ Y11 ≤ 35). (c) P (25 ≤ Y101 ≤ 35).