Robert F. Mulligan, Ph.D.
Department of Economics, Finance, & International Business
What is a Random Variable?

I. Random and Non-random Numbers
A. An algebraic equation as an example of a non-random variable
Slide 1: a Random Number Table
B. Gross characteristics of random number sequences 
1. Example: probability die 
2. Ad hoc example: unintended non-randomness
Slide 2: A Non-random Counterexample
C. Poor randomization in an ESP experiment 
II. From Random Number Sequence to Random Variable
Slide 3: 1000 Observations of a Uniform Random Variable
A. Some examples of Random Number Sequences 
1. Multiplicative congruential sequences 
2. Fibonacci sequence divided by a modulus 
Slide 4: A Histogram of Slide 3
B. Converting a sequence into an R.V. 
III. The Normal or Gaussian Distribution
Slide 5: 1000 Observations of a Normal or Gaussian Random Variable
A. Range and bounds
Slide 6: A Histogram of Slide 5
B. The classic bell curve shape 
IV. The Cauchy Distribution
Slides 7 through 9: Transforming a Uniform R.V. into a Cauchy R.V.
A. Range, bounds, and variance
Slide 10: A Histogram of Slide 9
B. Normal v. Cauchy characteristics
V. Deterministic v. Non-deterministic processes
Slide 11: A Manufacturing Process
Informational efficiency and very complex deterministic or chaotic processes