# COMPSCI 70 Chapter Notes - Chapter 20: Probability Distribution, Cumulative Distribution Function, Sample Space

## Document Summary

To find the probability of an event, sum up the probabilities. In continuous probability, one sample point has 0 probability ( ) Fubini"s theorem: means you integrate the inside with repect to first, and then the outside with respect to. Intervals are subsets of the sample space therefore, intervals are events probability density function (pdf) - the distribution of a real-valued random varialbe is given by. The integral of equalling 1 ensures that it defines a valid distribution (since the sum of probabilites in a distribution must always be 1) The area under the pdf curve is 1 because the sum of probability in a sample space is always 1. This property must hold because a probability of an event is always non -negative. The probability of an interval is proportional to its length. Pdfs are continuous probability distributions (pdfs give probabilities for continuous random variables) Pdfs have no meaning in the real world (cannot be formed intuitively) ii. i.