The Student’s t-distribution is often used for analyzing the properties of small samples. You use the binomial distribution when a random process consists of a sequence of independent trials, each of which has only two possible outcomes. Mostly that chapter focused on the binomial experiment. On the other hand, a fretless bass features a continuous distribution of notes; not only can she play an F and an F-sharp, but she can play any tone in between. Have questions or comments? In business applications, variables such as stock returns are often assumed to follow the normal distribution. Some of the most widely used continuous probability distributions are the: The normal distribution is one of the most widely used distributions in many disciplines, including economics, finance, biology, physics, psychology, and sociology. The geometric distribution is related to the binomial distribution; you use the geometric distribution to determine the probability that a specified number of trials will take place before the first success occurs. The probability of observing any single value is equal to $0$ since the number of values which may be assumed by the random variable is infinite. A probability distribution may be either discrete or continuous. Photo by Tim Stellmach. This means that the majority of the population has a height or weight close to the central mean (the peak of the distribution). We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Chapter 7 Continuous Probability Distributions 134 For smaller ranges the area principle still works; for example P()0