L05.7 Geometric Random Variables
The last discrete random variable that we will discuss is the so-called geometric random variable. It shows up in the context of the following experiment. We have a coin and we toss it infinitely many times and independently. And at each coin toss we have a fixed probability of heads, which is some given number, p. This is a parameter that specifies the experiment. When we say that the infinitely many tosses are independent, what we mean in a mathematical and formal sense is that any finite subset of those tosses are independent of each other. I'm only making this comment because we introduced a definition of independence of finitely many events, but had never defined the notion of independence or infinitely many events. The sample space for this experiment is the set of infinite sequences of heads and tails. So a typical outcome of this experiment might look like this. It's a sequence of heads and tails in some arbitrary order. And of course, it's an infinite...