5-1 Section 5: Continuous Random Variables Recall that a random variable is a function that assigns a real number to each outcome in a sample space. If the random variable can take on any value in some interval of real numbers, then it is called a continuous random variable. Discrete random variables most often arise from processes which involve counting, while continuous random variables typically arise from measurements. In this chapter we shall study basic properties of continuous random variables and their probability distributions. The Probability Density Function The first condition above simply states that the function must be nonnegative for all x, which will ensure that all associated probabilities are also nonnegative. The second property listed above