Probstat/notes/random variables

In many cases, after we perform a random experiment, we are interested in certain quantity from the outcome, not the actual outcome. In that case, we can define a random variable, which is a function from the sample space to real numbers, to represent the random quantity that we are interested in.

For example, consider the following experiment. We toss two dice. Let a random variable X be the sum of the values of these two dice.

A random variable X also induces events related to it. For example, we can consider the event that X=10.