The "Normal" Distribution
Of course, life is more complex than flipping coins and omniscient dictators are hard to find, but the basic reasoning does not change. Many things in life are examined statistically and for the past 350 years a very useful and powerful tool has been used for such inquiries. It is called a probability distribution function (pdf) and it looks like this:
All this does is provide a graphical representation of all the outcomes that can happen, arranged in order of the product of their probabilities times their payoffs. The peak occurs where the most likely is located, which on the x-axis is the expectation. For this illustration the expectation is zero. There is a dispersion of possibilities around the expectation that accounts for the area under the curve that is away from the center. This is known as "variance".
