Original article was published on Artificial Intelligence on Medium

“

The determination of the value of an item must not be based on the price, but rather on the utility it yields. There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man.” — Daniel Bernoulli

## Index

0.* *Dear Statistics Journal1. Introduction to Probability

**2.**

**The Monty Hall Problem**

*3. Gambler’s Fallacy*

4.

**St. Petersburg Paradox**

Before we get to the good stuff, let’s knock out a few useful concepts:

. Random Variables

. Expected Value

. Expected Utility

# Random Variables

A random variable *is a function *that maps the outcome of a random process to a real number.

E.g., say we have the random process of flipping a fair coin. X is essentially a function that maps values of the sample space ({Heads, Tails}) to a real number. In a sense, we are quantifying the state space of outcomes. As seen in **Fig 1**, we assign the values Heads=0 & Tails=1 and X is our random variable for this particular process.

# Expected Value

Expected value is the average value of a random variable over a large number of experiments