## 3.4 The Normal Distribution

#### The Standard Normal Distribution

- The standard normal distribution has the following probability density function

f(x)=\frac{1}{\sqrt{2 \pi}} e^{-\frac{1}{2} x^{2}}

and the domain is R.

- The graph of f(x) is shown at the right. Notice that it is symmetric over x=0

- If a random variable X follows the standard normal distribution, then we would denote X \sim N(0,1).

- Note that standard normal distribution is a special case of normal distribution, with a mean 0 and variance 1. Therefore, this explains the N(0,1) written above.

- The standard normal distribution also have some important graphical features: