Lesson 3

As can be seen, the distribution loses information about the outcomes and their probabilities. In particular, this means that different variables can have the same distribution. Moreover, they do not necessarily have to be defined on the same probability space. It is also easy to see that the distribution of a random variable is a probability distribution (outcomes are the values taken by the variable with corresponding probabilities). Despite the fact that a random variable is defined on a probability space, often we do not need the probability space itself: we will only be interested in how the random variable is distributed.