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Suppose that a stock price S follows geometric Brownian motion with expected return (mu) and volatility (sigma): dS = (mu)Sdt + (sigma)SdZ. 1. Please verify

Suppose that a stock price S follows geometric Brownian motion with expected return (mu) and volatility (sigma): dS = (mu)Sdt + (sigma)SdZ.

1. Please verify that S at time T is lognormal distributed.

2. Assume that stock price is currently 20. Its expected return and volatility are 10% and 20%, respectively. What is the probability that the stock price will be greater than 30 in 9 months?

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