Expectation of discrete random variables
Expectation of discrete random variables¶
Let \(X\) be a discrete random variable taking values \(0,1,2,\dots\). The expectation of \(X\) is defined by:
\[
\mathbf{E}[X] = \sum_x xp(x),
\]
where \(p(x)\) is the PMF and the summation is over all discrete values of \(X\).
Note
The expectation of a random variable is also known as the mean of the random variable.
You can think of the expectation as the value one should “expect” to get. However, take this interpretation with a grain of salt because the expectation may not even be a value that the random variable can take… Let’s look at some examples.