How can you estimate the parameters of a normal distribution?

1 Answer
Bill K.
Jan 22, 2016

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.

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