Normal Distribution

Central Limit Theorem
Normal Distribution
Standard Scores
The Sampling Distribution of the Sample Mean

Definition

We say that an random variable is normally distributed, , if its p.d.f. is:

where:

is the standard deviation
is the mean or expected value

A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable, distributed in a way shown below.

Figure

A plot of the normal distribution (bell curve) where each band is the width of 1 standard deviation.

The curve is symmetrical around , which is the mean, median and mode.

Important

Remember the values , , and . These are very important.

of observations are between
of observations are between
of observations are between

Support and CDF

Support:

Expected Value and Variance

We could use an MGF

Standard Normal Distribution

Definition

A standard normal distribution has mean () of and standard deviation () of .

we'll use and instead of and sometimes.