Standard Normal PDF

Notes:

• A random variable is said to have a standard normal distribution if its probability density function is given by the above formula.
• The characteristic bell-shaped feature of a normal distribution is seen in the following plot of this very important pdf.
• As can be seen, the above density function is symmetric about 0, the mean of the standard normal distribution.
• The variance of a standard normal distribution is 1. It is well-known that a random variable with such a distribution is almost certain to be within three standard deviation of its mean, i.e., This is evident from the above plot since we see that almost all the area under the standard normal pdf is within the stated bounds.
• Two important related functions are the standard normal cdf and quantile functions.