Chapter 16: Discrete and Continuous Random Variables

A special terminology is useful for discussing probability distributions of numerical scores. In this chapter we will discuss discrete and continuous random variables with some associated distributions. Some of the material in this chapter is used with permission from Stuart, A., Ford Motor Company.

INTRODUCTION

A random variable (RV) is a real valued number assigned to each individual sample, S _i , according to some function X(S _i )

• Individual sample, S _i

• Discrete real-valued number, X _i .

• An individual sample cannot be assigned two random values.

• Range of real- numbers is typically finite.

x = {X _i } i = 1, 2, 3, ..., M

or

x = {X ₁ , X ₂ , X ₃ , ..., X _M }

Assume an ascending order of magnitude: X _i-1 < X _i < X _i+1 . Pictorially, this may be shown as: