| Binomial | Multinomial | Continuous | Arbitrary |
| \(EX = P(x) * X\) | \(EX = \displaystyle\sum_{i}^{N} P(x_i) * x_i\) | \(EX = \displaystyle\int_{-\infty}^\infty x f(x) dx\) | \(EX = \displaystyle\sum_{i} g(x) * f(x)\) |
| If probability of winning a lottery (getting a prize) is \(0.1\), and you buy \(20\) tickets, then the expected value (number of prizes) is \(0.1*20 = 2\), i.e. \(2\) prizes. | blabla | blabla | blabla |
About this series
This is an article from the series about statistics (and probability theory). The motivation behind this series is to retain knowledge while taking courses, reading books and articles. I write articles about something that I missed before, found interesting or possibly useful to me in the future. These articles do not constitute a course, they are just a collection of my personal study notes or summaries on different topics related to statistics.
Expected value
In simple terms, the expected value is the average value that we expect to get if we repeat a random process many times. It is a measure of the central tendency of a random variable. So, to calculate expected value, we need to understand what is a random variable in our case.
Notation
- Random variable: \(X\)
- Expected value of \(X\): \(E[X]\) (as functional), \(E(X)\) (as function) or \(EX\).