Probability Density Function (PDF) is a statistical measure used to gauge the likely outcome of a given discrete or continuous variable. It is often used for financial investments to measure the potential risk/reward of a particular security or fund in a portfolio. PDFs are often represented graphically as a bell-curve, with the probability of the outcomes lying below the curve.

A discrete variable is one that can be measured exactly, for example, the price of a stock or ETF. The likelihood of a particular value coming up can be expressed as a probability. The probability of one particular stock in a portfolio having a particular price can be derived using PDFs.

A continuous variable is one that can have infinite values, the most common example being normal distribution. Normal distributions are commonly used to understand the probability of a particular outcome, as they form a bell-shaped curve. The overall probability of a particular outcome being observed is the area beneath the curve, so a larger bell-curve equates to a higher probability of a larger range of values being observed. Any occurrence in which the probability is greater than zero is considered a “true” event.

PDFs provide investors and traders with a useful tool for understanding the risk/reward of a particular strategy. By plotting the probability of different outcomes, traders and investors are able to make informed decisions based on the expected probability of a particular event occurring. For example, if a trader expects a particular stock to go up in value, they can calculate the probability of it rising using a PDF.

In summary, PDFs are a powerful statistical tool that can be used to understand the probability of discrete and continuous values. They enable investors and traders to make informed decisions based on the expected probability of a particular outcome occurring. By understanding the area beneath the curve, traders can gauge the potential reward and risk of any given strategy.