Shape of a probability density function

A probability density function is usually a fairly smooth curve, though a single sample histogram provides limited information about its likely shape.

sample —> popn?

Normal distributions

One flexible group of continuous probability density functions is the family of normal distributions. Normal distributions:

Changing the parameters µ and σ changes where the distribution is centred and its spread, but its shape remains otherwise the same.

The parameters are often estimated from a sample. Details will be given later, but the resulting normal pdf will be close in shape to a histogram of the sample data.