Cumulative Distribution Function

What is the Cumulative Distribution Function?

The cumulative distribution function integrates the area under the curve. Integration in this respect is just a fancy way of saying, adding up the area under the curve, adding the individual probabilities. The cumulative distribution involves adding the probabilities of each outcome starting from the left-hand side of the x axis moving to the right. It gives the total area under the curve to the left of any given point that we choose. Therefore, the area to the right of that point will be 100% minus the area to the left. It climbs up and eventually tapers off at 100%.

What are the uses of the CDF?

It allows us to answer questions such as what’s the probability of an outcome being x, less than x or greater than y, or, somewhere in between x and y etc.

How do the probabilities differ for continuous variables?

For continuous variables, where these intervals are infinitely small, each individual probability will be very close to zero and the total area under the curve will be very close to 100%.

How is this visually represented?