Continuous Probability Distributions

So far we have looked at discrete probability distributions where values can be assigned to every outcome in the sample space.

For continuous distributions, probability is represented as a function called the probability density function, or density function. These functions must be greater than zero, and must not have an area greater than 1 under their curves. The functions are called "density functions" because they will graph a smooth curve showing values that are most likely or "dense".

Look at the example below which shows a normal curve:


We can see very quickly that observations are most "dense" between 40 and 50. To find out the exact probability of a value being between 40 and 50, we must calculate the area of the region between 40 and 50. The same is true to find the probability of a value being less than 40. We must calculate the area under the curve that is less than 40. Thus we calculate the area under the curve for any probabilities we want to find.