R Tutorial: Expected value and variance

Want to learn more? Take the full course at https://learn.datacamp.com/courses/foundations-of-probability-in-r at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- When we talk about a probability distribution, we're often interested in summarizing it into a few descriptive statistics. Two of the most interesting properties are where the distribution is centered, and how widely spread out it is. We describe these with the expected value and the variance. The expected value is the mean of the distribution. If you imagine we drew an infinite number of values from the distribution, the expected value is what the average of all those would be. This puts it right at the center of a distribution. Let's try to find the expected value of the binomial distribution with size 10, and probability point-5. We can't draw an infinite number of values, but we can draw a lot of them. As you've done in the exercises, we can use rbinom to simulate one hundred thousand draws with size 10 and probability point-5, then use the mean() function to take the average of these draws. We see the average is very close to 5. That's the "center" of the distribution if we displayed it as a histogram. If we tried sampling from a binomial with size 100 and probability point-2, we find that the mean is very close to 20. As you might notice from these examples, there's a general rule: we can get the expected value of a binomial distribution by multiplying the size (or the number of coins), by the probability each is heads. The expected value measures the center of the distribution, but we also want a measure of how spread out the results are. Statisticians use the variance to measure this. Variance is the average squared distance of each value from the mean of the sample. The variance isn't quite as intuitive as the mean, but it has useful mathematical properties that will become clear in this course. R provides the var() function to