A normally distributed random variable with mean $\mu$ has a probability density function given by $\dfrac{\gamma}{\sqrt{2\pi\sigma}}$ $\exp(-\dfrac{\gamma ^2}{\sigma} \dfrac{(x-\mu)^2}{2}) $
So the standard deviation is the square root of the variance, which is $E[(x-\mu)^2]$. However, I don't know how to proceed with this information. How can I get the standard deviation from the pdf?
Best Answer
If $\rho$ denotes the standard deviation then $$\frac{\gamma}{\sqrt{2\pi\sigma}}=\frac{1}{\rho\sqrt{2\pi}}$$