Chapter 8, Problem 8.11P

Many people believe that the daily change of price of a company’s stock on the stock market is a random variable with mean 0 and variance 2. That is, if Y represents the price of the stock on the nth day, then $Y_n=Y_{n-1}+X_{n}n\ge 1$ where $X_1,X_2,\mathrm{...}$ are independent and identically distributed random variables with mean 0 and variance ${\sigma }^2$. Suppose that the stock’s price today is 100. If ${\sigma }^2=1$, what can you say about the probability that the stock’s price will exceed 105 after 10 days?