The price of a stock is governed by a log normal distribution with the expected growth rate μ=.12, volatility, σ=.2. The initial price is $75. I have already calcuated: E(stock price after 6 months) = 79.64 V = 128.12 σ = 11.32 How do I show that the probability of a loss after 6 months is 0.3372? Thanks. 2.$\displaystyle \ln S_{T} \sim \phi \left[\ln S_{0} + \left(\mu - \frac{\sigma^{2}}{2} \right)T, \sigma \sqrt{T} \right] $So I think$\displaystyle P \left(\text{loss after six months} \right) = \Phi \left(\frac{x - 79.64}{\sigma \sqrt{T}} \right) $where$\displaystyle \text{mean} = \ln S_{0} + \left(\mu - \frac{\sigma^{2}}{2} \right)T $. 3. so, is x the mean? Just to clarify, is the μ and σ that I use to calculate the mean the ones that I calculated and not the ones that are given? 4. Originally Posted by taypez so, is x the mean? Just to clarify, is the μ and σ that I use to calculate the mean the ones that I calculated and not the ones that are given? Mean:$\displaystyle \mu$Standard deviation:$\displaystyle \sigma\$