# When to use pdf and cdf statistics

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## Probability Density Functions (PDFs)

Typical Analysis Procedure.

### Probability density functions

The cumulative distribution function CDF calculates the cumulative probability for a given x-value. Use the CDF to determine the probability that a random observation that is taken from the population will be less than or equal to a certain value. You can also use this information to determine the probability that an observation will be greater than a certain value, or between two values. For example, soda can fill weights follow a normal distribution with a mean of 12 ounces and a standard deviation of 0. The probability density function PDF describes the likelihood of possible values of fill weight.

Say you were to take a coin from your pocket and toss it into the air. While it flips through space, what could you possibly say about its future? Will it land heads up? More than that, how long will it remain in the air? How many times will it bounce? How far from where it first hits the ground will it finally come to rest? For that matter, will it ever hit the ground?

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. I am learning stats. On page 20, my book, All of Statistics 1e, defines a CDF as function that maps x to the probability that a random variable, X, is less than x. We have that I am a little confused about how to characterize the most important difference between them.

## Probability Density Functions (PDFs)

Cumulative distribution functions are also used to specify the distribution of multivariate random variables. The proper use of tables of the binomial and Poisson distributions depends upon this convention. The probability density function of a continuous random variable can be determined from the cumulative distribution function by differentiating [3] using the Fundamental Theorem of Calculus ; i. Every function with these four properties is a CDF, i. Sometimes, it is useful to study the opposite question and ask how often the random variable is above a particular level.

Recall that continuous random variables have uncountably many possible values think of intervals of real numbers. Just as for discrete random variables, we can talk about probabilities for continuous random variables using density functions. The first three conditions in the definition state the properties necessary for a function to be a valid pdf for a continuous random variable. So, if we wish to calculate the probability that a person waits less than 30 seconds or 0. Note that, unlike discrete random variables, continuous random variables have zero point probabilities , i. And whether or not the endpoints of the interval are included does not affect the probability. Recall Definition 3.

For a continuous random variable, we cannot use a PDF directly, since for why the pdf is the derivative of the cdf, refer to a statistical textbook.

This tutorial provides a simple explanation of the difference between a PDF probability density function and a CDF cumulative distribution function in statistics. There are two types of random variables: discrete and continuous. Some examples of discrete random variables include:.

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