We look at the definitions first.
A continuous random variable, X, has a probability density function (PDF), if and for all events A
The CDF and PDF are related by
It is good to know that we have
We X has a normal distribution, , and . And while
We also have the log-normal distribution, and . Here, and . The log-normal distribution is very important in financial applications, for starters, the Black Scholes Equation.