Expectation and variance

Expectation, often called the average or mean, is the long-term average value you'd expect if you could repeat a random process many times. Variance measures how much those values change or spread out around the average; a small variance means outcomes are similar to the average, while a large variance indicates more variability. Both concepts help us understand and predict the behavior of uncertain events, such as the results of a game or the fluctuations in stock prices, by summarizing their typical value and how much they tend to vary.