 Let's consider a second example of total expectation. Let's say we have a computer system with 1,000 users on that system, and the users chose a password. And we want to know something about, well, what's the average length of a password that the users choose? So we look at the password lengths chosen by users and count how many users chose passwords with a particular number of characters. And we collect the following data where we see that 150 users chose six character passwords, 500 users chose seven characters, turned out no one chose eight character passwords, 259 characters, and 100 users chose 10 character passwords. So again, we have mutually exclusive events in this case in that a user cannot choose two different length passwords. And the set of events are exhaustive in that we have 1,000 users, and we cover all those 1,000 users in terms of selecting passwords. So we can quite easily calculate the expected value for the system. That is the expected password length, or the average password length. We can calculate it as we have the probability of selecting the expected value of the first set of event is that we get six characters. Times by the probability of that, we have 150 users out of 1,000 in total. And the expected value of the second event selects seven character password times by our 500 users over 1,000, which is 50%, or 0.5, 9 times 250 over 1,000 plus 10 times 100 divided by 1,000, or 0.1. And with a calculator, we can calculate that. And we calculate 6 times 0.15 plus 7 times 0.5 plus 9 times 0.25 plus 10 times 0.1, 7.65. That is, on average, the users choose a password length of 7.65 characters.