So now, let's look at an example that applies the square root law. We toss a fair coin 100 times, how many tails do we expect to see and what's the give or take number? This is an example where we count. We count how many tails we're going to see in 100 tosses. So we'll introduce labels, where a 1 stands for tails and a 0 stands for heads. Then, we simulate this 100 tosses either by literally tossing a coin 100 times or by using a computer, and in each case, we have the probability of getting a 1 is a half and the probability of getting a 0 is also a half. Because we have 0 and 1 labels, we find that the number of tails in the 100 tosses equals the sum of the 100 draws. So then we can use our formula for the expected value of the sum and it says, it's the sample size which is 100 times Mu. Now the formula for Mu on the previous slide says, it's the sum of all outcomes times their probabilities and that is a half. So the expected value of the sum is 50 and that would be our answer, we expect to see 50 tails. Now the give or take number is the standard error. So we have to look at the standard error of the sum and the formula says, this is square root sample size times Sigma. So we have to figure out what Sigma is, the formula for Sigma square is, take each outcome, subtract off the mean, square it, times the probability which is a half, and then we have to do that for the second outcome, and we find this is one-quarter. So now since we are looking at Sigma, not Sigma squared, we get 10 times one-half instead of a quarter and that is 5. So our answer would be, that we expect to see 50 tails, give or take five. By the way, if we did this for the percentage of tails, then the formula for the percentage says, we take Sigma over square root of sample size and that is 0.05, or 5%. So in terms of percentages, our answer would be, we expect to see 50% tails give or take 5 percentage points.