By Leroy A. MacColl (ed.)

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A probability distribution is a mathematical model that maps all of the outcomes that a random variable can take to speciﬁc probabilities. It thereby gives us a complete listing of all possible outcomes of an experiment together with their probabilities. In this sense probability distributions provide a complete representation of the 30 ENERGY RISK MODELING uncertainty surrounding every potential outcome of a random variable – it informs us what outcomes are possible and how likely they are. There are two broad types of probability distribution, those for discrete random variables known as probability mass functions and those for continuous random variables know as probability density functions.

2 ENERGY RISK MODELING Transformation to the standard normal distribution If X is normally distributed with mean µ and variance σ 2 it can be transformed into a standard normal random variable Z via Z= X−µ . σ The transformed random variable Z, also known as a standardized variable or standard normal variable has a mean of zero and a variance equal to 1. Standardized values are sometimes called Z scores. What is the value of using a Z score? Z scores reﬂect the number of standard deviations above or below the mean that a particular value lies.

Brower, Michael (1994) Cool Energy: Renewable Solutions to Environmental Problems. Massachusetts, MIT Press. Smil, Vaclav (1994) Energy in World History. Westview Press, Colorado. Yergin, Daniel (1992) The Prize: The Epic Quest for Oil, Money, and Power. Touchstone, New York. Rudolph, Richard and Ridley, Scott (1986) Power Struggle: The Hundred-Year War over Electricity. Harper and Rowe, New York. G. ” He made no mention of ﬁnancial risk management because the ﬁnancial market place was still in its infancy.