Question

How can you estimate the parameters of a normal distribution?

Answer 1

Use the sample mean `bar{x}` and the sample standard deviation `s` to estimate the mean `mu` and standard deviation `sigma` of the normal distribution you wish to use.

Explanation:

The normal distribution has probability density function (pdf) `f(x)=1/(sigma sqrt{2pi})e^{-(x-mu)^2/(2sigma^2)}`. The parameter `mu` is its mean and the parameter `sigma` is its standard deviation.

If you have data from a random sample and compute the sample mean `bar{x}=(x_1+x_2+x_3+cdots+x_n)/n` and the sample standard deviation `s=sqrt{((x_1-bar{x})^2+(x_2-bar{x})^2+cdots+(x_n-bar{x})^2)/(n-1)}`, these will be good estimates for `mu` and `sigma` when your sample size `n` is sufficient large.