The cumulative distribution function for any random variable X, denoted by F( x), is the probability that X assumes a value less than or equal to x:Р”Р‡ ( x ) = Pr ( X РІвЂ°В¤ x )

To make this definition more precise, we recall the definition from Section 1.4 of a cumulative distribution function (CDF) that was given for any random variable. Example 1: Flipping a coin (discrete) Flipping a coin is discrete because the result can only be heads or tails. Before we dive into continuous random variables, letРІР‚в„ўs walk a few more discrete random variable examples. These include Bernoulli, Binomial and Poisson distributions. For example, we can define a continuous random variable that can take on any value in the interval. A number of distributions are based on discrete random variables. This is not one of the named random variables we know about. answer: (d) This is dierent from problem 1 because we are combining Bernoulli(p) r.v.РІР‚в„ўs with Bernoulli(q) r.v.РІР‚в„ўs. What is set of individual possible values-for example, the positive integers 1, 2, 3 in finance. Each binomial random variable is a sum of independent Bernoulli(p random variables, so their sum is also a sum of Bernoulli(p) r.v.РІР‚в„ўs. We previously defined a continuous random variable to be one where the values the random variable can assume are given by a continuum of values. Meaning of Discrete random variable explanation. If for example X is the height of a randomly selected person in British Columbia, or X is tomorrow's low temperature at Vancouver International Airport, then X is a continuously varying quantity.

In this chapter, we properly treat continuous random variables. In the previous chapter, we defined random variables in general, but focused only on discrete random variables.

Cdf of discrete random variable