Examples of Continuous Probability Distributions

Examples of continuous probability distributions:

The normal and standard normal

The Normal Distribution

f(X)

Changing shifts the

distribution left or right.

Changing increases or decreases the spread.

X

The Normal Distribution: as mathematical function (pdf)

f (x) =

1

-1( x-? )2

e 2

2

Note constants: =3.14159 e=2.71828

This is a bell shaped curve with different centers and spreads depending on ? and

The Normal PDF

It's a probability function, so no matter what the values of ? and , must integrate to 1!

+

1

-1( x-? )2

e 2 dx = 1

- 2

Normal distribution is defined by its mean and standard dev.

E(X)=? =

+

x

1

-1( x-? )2

e 2 dx

- 2

Var(X)=2 =

+

( x 2

1

e

-1( 2

x-?

)2

dx

)

-

?

2

- 2

Standard Deviation(X)=

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download