Mathematics — Probability · law-of-large-numbers-continuous
Problem
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).