Cumulative distribution function

Definition

The cumulative distribution function (CDF) of a random variable gives the probability that the variable takes on a value less than or equal to a specified number. It is a non-decreasing function that ranges from 0 to 1.

5 Must Know Facts For Your Next Test

1. The CDF for a discrete random variable is calculated by summing the probabilities of all outcomes up to and including a given value.
2. For continuous random variables, the CDF is obtained by integrating the probability density function (PDF).
3. The CDF of a binomial distribution can be found using tables, software, or cumulative binomial probability formulas.
4. CDFs are useful for finding percentiles and quantiles in probability distributions.
5. A stepwise graph represents the CDF of discrete distributions, while a smooth curve represents continuous distributions.

Review Questions

• What does the cumulative distribution function represent in probability theory?
• How do you calculate the CDF for a discrete random variable?
• What method would you use to find the CDF of a binomial distribution?

Related terms

Probability Density Function (PDF): A function that describes the likelihood of a random variable to take on a particular value.

Binomial Distribution: A probability distribution that summarizes the likelihood that a value will take one of two independent states under certain parameters.

Percentile: A measure indicating the value below which a given percentage of observations fall within a data set.