Python Tutorial : Expected value, mean, and variance

Want to learn more? Take the full course at https://learn.datacamp.com/courses/foundations-of-probability-in-python at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- Is there an outcome in the data that is more likely than others? How spread out is the data? Let's explore three metrics for measuring these attributes: the expected value, the mean, and the variance. A discrete random variable has finite outcomes. For instance, the roll of a die has only six possible outcomes. For discrete random variables, the expected value is the sum of the possible outcomes weighted by their probability. To calculate the expected value, each outcome is multiplied by its probability, and the products are summed. In simple terms, the expected value is a value where the probability will concentrate when you repeat the experiment. We multiply our tails outcome by its probability, 1 - p then we add the heads outcome, which is 1 multiplied by its probability, p, and we get the expected value p. The arithmetic mean is the sum of each outcome divided by the number of samples. It is based on data. We will see that the arithmetic mean of the outcomes converges to the expected value as we increase the number of random experiments. If we calculate the mean from many coin flips we will get a number near the probability of heads for that particular coin. In Python, we will use the describe function from the scipy dot stats library to get the mean: all we have to do is pass an array to the method to get its mean. If we repeat the experiment and make hundreds of fair coin flips we should get a number near 0.5. So, the more coins we flip, the more the sample mean of all the throws approaches the expected value If we add even more coin flips, it becomes even clearer that the sample mean tends to the expected value. That is the relationship between the expected value and the mean. This is known as the law of large numbe