L21.5 The Fresh Start Property
In this segment we develop some consequences of the independence assumption that we have made on the trials that constitute a Bernoulli process. These properties will be pretty intuitive, but they play an important role. They're helpful in solving problems, and they're also quite helpful in understanding the continuous time version of the Bernoulli process, namely the Poisson process that we will be studying later. So here's the story. We start with a Bernoulli processes with some parameter p. The process starts. A friend of yours watches the processes, and they observe the results of the different trials, let's say for five time steps. And at this time, right after time five, they call you into the room, and you start watching the rest of the process. What will you see? The first random variable that you will see is the result of whatever happens in this time slot, which is the sixth slot of the original process. The second random variable that you will s...