Probability Theory Probability Space To start our discussion of probability theory, we first need to define the concept of probability space. For a simple definition, the probability space of some probabilistic experiment is the set of...

The Cumulative Distribution Function 3.2.1 The Cumulative Distribution Function Definition 3.10The cumulative distribution function CDF of a random variable X is a function  given by Example 3.9: Say we toss a coin twice. Let X be the number of heads we observe....

Discrete Random Variables Random Variables Definition: In probability theory, the sample space of an experiment is the set of all possible outcomes of that experiment. Here, we will refer to the sameple space as , though you may also see...

Incompleteness Mathematicians love simplicity. Back around 1900, their dream was to create a world of math that was cleanly split in two. True statements would all be provable from axioms. The false statements, none of them...