# Probability Density Function

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Continuous distributions are constructed from continuous random variables which take values at every point over a given interval and are usually generated from experiments in which things are “measured” as opposed to “counted”.

With continuous distributions, probabilities of outcomes occurring between particular points are determined by calculating the area under the probability density function (pdf) curve between those points. In addition, the entire area under the whole curve is equal to 1.

Probability Density Functions
This tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equivalent to the area under the curve.
It also contains an example problem with an exponential density function involving the mean u which represents the average wait time for a customer in the example problem.
Examples:
1. Given f(x) = 0.048x(5 - x)
a) Verify that f is a probability density function.
b) What is the probability that x is greater than 4.
c) What is the probability that x is between 1 and 3 inclusive.

2. The average waiting time for a customer at a restaurant is 5 minutes. Using an exponential density function
a) Find the probability that a customer has to wait more than 7 minutes.
b) Find the probability that a customer will be served within the first 3 minutes.
Probability density functions for continuous random variables Probability density functions and continuous random variables How to calculate probabilities from density functions?

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