Cumulative distribution function (CDF)

Definition

A cumulative distribution function (CDF) represents the probability that a continuous random variable takes on a value less than or equal to a specific value. It is an integral of the probability density function (PDF).

5 Must Know Facts For Your Next Test

1. The CDF of a continuous random variable is always non-decreasing.
2. The CDF ranges from 0 to 1, where 0 represents the lowest possible value and 1 represents the highest possible value.
3. For an exponential distribution with rate parameter $\lambda$, the CDF is given by $F(x) = 1 - e^{-\lambda x}$ for $x \geq 0$.
4. The CDF can be used to find probabilities over intervals by subtracting the CDF values at the interval endpoints.
5. The derivative of the CDF with respect to its variable gives back the PDF.

Review Questions

• What does the cumulative distribution function (CDF) represent in statistics?
• How do you compute the CDF for an exponential distribution with rate parameter $\lambda$?
• What is the relationship between a PDF and a CDF?

Related terms

Probability Density Function (PDF): The function that describes the likelihood of a continuous random variable taking on a specific value.

Exponential Distribution:

A type of continuous probability distribution often used to model time until an event occurs, characterized by its rate parameter $\lambda$.

Rate Parameter ($\lambda$): A parameter in exponential distributions that determines how quickly events occur over time.