Probability and Expected Value

Expected value

It is the expected value of the random variable as an outcome of a random event. One could argue that over an infinite number of trials, the predicted average outcome is our expected value.

e.g. E(X) = u = 1/6?* (1 + 2 + 3 + 4 + 5 + 6) = 3.5

Note that 1/6 is the probability for each of the total 6 probable , equally likely, outcomes on a fair dice. And so it looks like average of all the outcomes is the expected value.

More specifically, expected value is a linear combination of outcomes and their respective probabilities a.k.a. weighted average of all the outcomes based on their probabilities.

Here, X is the random variable representing the outcome of throwing a dice and E(X) is the expected value of the outcome.

Expected value is also known as “long-run average” when estimated from results of long and, for all practical purposes, exhaustive trials.

If case you missed one of my previous article where I demonstrate a simple method of generating probability of each plausible outcome (i.e. {1, 2, 3, 4, 5, 6}) of throwing a fair dice using a video on using random function in MATLAB, do consider reading it.?

Following doodle works out expected value for the generated probability distribution from my past article:

Please feel free to share your feedback and suggestions. If you enjoyed reading this, do consider giving the article a thumbs up. And I will see you next time!

-Sanjay