A statistical expression or function that determines the probabilities of occurrence of different possible outcomes for a continuous random variable, such as actively traded instruments/ securities, exchange-traded products (e.g., ETF) and derivative products. A
probability density function (PDF) completely characterizes the distribution of a continuous random variable. It is one of two key methods used to define the probability distribution of a random variable. The former involves assigning a probability to each value that the variable (by necessity a discrete variable) can take, while the latter (PDF) is based on assigning probabilities to intervals of values that the variable (a continuous variable) can take.
![PDF](https://fincyclopedia.net/wp-content/uploads/2024/07/pdf.png)
In the diagram above, the blue line (continuous) is the PDF of a normal random variable, and the read area constitutes the probability that the random variable takes a value in the interval between -2 and 2.
It shall be noted that the probability density function characterizes the distribution of a continuous random variable, and hence it is not a probability of occurrence. In contrast, the probability mass function characterizes the distribution of a discrete random variable.
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