A function that indicates the observable values of a discrete random variable and associated cumulative probabilities is called the cumulative distribution function.

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

Definition and Probability Distributions A random variable is a real-valued function defined on the sample space of an experiment. A discrete random variable can only take on a finite or countably ...

Given a pair of discrete random variables X and Y, the joint mass function f (x, y) = P (X = x and Y = y). Given a pair of continuous random variables, we call f (x, y) a bivariate probability density ...

A random variable that counts the number of 1's in 18 dice rolls is similar to one that counts the number of heads in 100 coin tosses or the number of females in 50 births. The probability functions ...

We approximate mixture and compound probability distributions with cosine series. Enormous precision and computational speed are the qualities of the function estimates here obtained. We also develop ...

Some of the commonly used continuous random variables are introduced below. Continuous random variables are introduced by giving either their pdf or cdf. In dealing with continuous random variables, ...

Continuous random variables Continuous random variables A continuous random variable is a type of variable that can take on any value within a given range. Unlike discrete random variables, which have ...