Let $\mathbb{E}(X)$ be the expected value of a discrete random variable $X$. How do I interpret $\mathbb{E}(X)$?
One of the way to interpret $\mathbb{E}(X)$ is to consider a large number of trails of the experiment, and then take the arithmetic mean of the values taken by $X$. Equivalently, we can think of $\mathbb{E}(X)$ as the center of mass of the distribution of $X$. Are there any other better ways to interpret $\mathbb{E}(X)$ ?
For instance, if we have $X\sim\text{Geom}(p)$, interpreted as the number of Bernoulli trials needed to get one success, then we have $\mathbb{E}(X)=1/p$. If $p=1/10$, then we have $\mathbb{E}(X)=10$. This would mean that, on average it would take $10$ trials to get the first success. I am having a hard time to digest this!
Best Answer
The ways you suggested are certainly correct. Another way to interpret $E(X)$ is as the value you would most often see if you were to observe $X$ over a long period of time.