# Homework Help: Calculus and Statistics

1. Feb 6, 2005

Hello all

Let's say we have $$\frac{1}{\sqrt{2\pi}} e^{\frac{-1}{2\phi^2}}$$ where $$\phi$$ is a standarized normal variable. Let $$R_{i} = \frac{S_{i+1} - S_{i}}{S_{i}}$$Also let's say we have a time step $$\delta t$$ and the mean of the returns scaled with the timestep.Then mean = $$\mu\delta t$$

Then why does $$\frac{S_{i+1}-S_{i}}{S_{i}} = \mu\delta t$$? Isn't this supposed to be a z-score? Also suppose we want to know how the standard deviation scales with the timestep $$\delta t$$ The sample standard deviation is $$\sqrt{\frac{1}{M-1}\sum^M_{i=1}(R_{i}-R)^2}$$ How do we use this to get standard deviation = $$\sigma\delta t^{\frac{1}{2}}$$

Also why does $$R_{i} = \mu\delta t + \sigma\phi\delta t ^{\frac{1}{2}}$$?

Thanks

Last edited: Feb 6, 2005
2. Feb 6, 2005