L06.2 Variance
We have introduced the concept of expected value or mean, which tells us the average value of a random variable. We will now introduce another quantity, the variance, which quantifies the spread of the distribution of a random variable. So consider a random variable with a given PMF, for example like the PMF shown in this diagram. And consider another random variable that happens to have the same mean, but it's distribution is more spread out. So both random variables have the same mean, which we denote by mu, and which in this picture would be somewhere around here. However, the second PMF, the blue PMF, has typical outcomes that tend to have a larger distance from the mean. By distance from the mean what we mean is that if the result of the random variable, its numerical value, happens to be, let's say for example, this one, then this quantity here is X minus mu is the distance from the mean, how far away the outcome of the random variable happens to be from the...