Statistical Inference: A Short Course

6.1 The Continuous Probability Distribution

A probability distribution is termed continuous if its underlying random variable is continuous, that is, if can assume an infinite or uncountable number of real values over some interval. Such variables are “measured” in terms of distance, temperature, weight, time, and so on. For instance, = time between arrivals of vehicles at a toll booth is a continuous random variable. Also, if two points and are chosen at random on a real line segment of length L (Fig. 6.1), then the distance (the absolute value¹ of minus ), can assume an infinite number of values ...