Introductory Mathematics and Statistics for Islamic Finance, + Website

Chapter 11Introduction to Probability Theory: Axioms and Distributions

Islamic finance uses probability theory and statistics, including econometrics. These disciplines are widely used in many other sciences such as physics, medicine, biology, engineering, communications, economics, management, and insurance. We encounter deterministic as well as probabilistic events. You may predict with certainty that the sun will rise tomorrow, or the sun will set at 7.21 p.m. on March 20 of every year in Washington, D.C. However, you may not be as certain whether it will rain next year on March 20 in Washington, D.C. The best you can do is to look at the record of the rainfall in Washington, D.C., in the past, say during the past 100 years, and if you realize it rained on 42 out of 100 days, then you may state that based on past experience it may rain on March 20 next year with a probability of 42 percent.

Probability theory is the science of randomness. It formulates models to study random events and random variables, and emit probabilities as regards the occurrences of random events. Statistics is the science of collection of data about specified variables; it formulates models for analyzing sampled data.

Finance involves risk and uncertainty. Assets are risky and may be highly volatile. Each return has a risk. Investors form expectations regarding the payoffs of their investment or hedging strategies. A firm may invest in new plants or products; however, actual payoffs are contingent ...