# Homework Help: Mean, squared mean and standard deviations of a gaussian

1. Jan 30, 2010

### sebastian616

1. The problem statement, all variables and given/known data
find <x>, <$$x^{2}$$> and $$\sigma$$ of the probability distribution;
$$\rho(x)$$ = $$\sqrt{\frac{\lambda}{\pi}}e$$$$^{-\lambda(x-a)^{2}}$$

2. Relevant equations

As shown above

3. The attempt at a solution

I know that I can simply take the mean value (a) and the standard deviation(1/2$$\sigma$$) from the fact that this equation is a gaussian, however wanted to know if there was a more rigorous method of calculating these figures than just saying what it is from the gaussian distribution.