Notes on Continuous Random Variables

Continuous random variables are random quantities that are measured on a continuous scale. They can usually take on any value over some interval, which distinguishes them from discrete random variables, which can take on only a sequence of values, usually integers. Typically random variables that represent, for example, time or distance will be continuous rather than discrete. Just as we describe the probability distribution of a discrete random variable by specifying the probability that the random variable takes on each possible value, we describe the probability distribution of a continuous random variable by giving its density function. A density function is a function f which satisfies the following two properties: 1. f(x) ≥ 0 for all x.