B E 2100 Chapter Notes - Chapter 4.1-4.2: Probability Density Function, Probability Distribution

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27 Jun 2018

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BE 2100 Chapter 4.1 notes

Let X be continuous rv. Then the probability distribution or probability density function (pdf) of X

is a function f(x) such that for any two numbers a and b with a≤b,

That is, the probability that X takes on a value in the interval [a,b] is the area above this interval and

under the graph of the density function.

A continuous rv X is said to have a uniform distribution on the internal [A,B] if the pdf of X is

BE 2100 Chapter 4.2

The cumulative distribution F(x) for a continuous rv X is defined for every number x by

For each x, F(x) is the area under the density curve to the left of x.

Using F(x) to compute probabilities

oLet C be a continuous rv with pdf f(x) and cdf F(x). Then for any number a,

And for any two numbers a and b with ab

Obtaining f(x) from F(x)

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