L21.3 Stochastic Processes
We have said that the Bernoulli process is the simplest stochastic processes there is. But what is a stochastic process anyway? A stochastic process can be thought of as a sequence of random variables. Now, how is this different from what we have doing before, where we have dealt with multiple random variables? Well, one difference is that here we're talking about an infinite sequence of random variables. And that complicates things to a certain extent. Now, what does it take to describe a stochastic process? We should specify the properties of each one of those random variables. For example, we might be interested in the mean, variance, or PMF of those random variables. For the case of the Bernoulli process, this would be easy to do. We know what the expected value is. We have a formula for the variance. And we have a fairly simple PMF. There's probability p that X is equal to 1 and probability 1 minus p that X equals to 0. But this is not enough. We also need to...