ABSTRACT
This chapter discusses continuous r.v.s, which can take on any real value in an interval. It looks at properties of continuous r.v.s in general. The chapter presents three famous continuous distributions—the Uniform, Normal, and Exponential—which, in addition to having important stories in their own right, serve as building blocks for many other useful continuous distributions. It also discusses a remarkable property of the Uniform distribution: given Unit random variables (r.v.). The Normal distribution is a famous continuous distribution with a bell-shaped probability density function (PDF). The Exponential distribution is the continuous counterpart to the Geometric distribution. Continuous r.v.s that is independent and identically distributed has an important symmetry property: all possible orderings are equally likely. A continuous r.v. can take on any value in an interval, although the probability that it equals any particular value is 0. The cumulative distribution function of a continuous r.v. is differentiable, and the derivative is called the PDF.
