A cumulative distribution function (CDF) is a function that shows the cumulative probability of a random variable being less than or equal to a given value. It can be thought of as the running total of probabilities up to a certain point.
A probability density function (PDF) is a function that shows the relative likelihood of a random variable taking on a specific value. It represents the probability distribution of a continuous random variable.
The main difference between a CDF and a PDF is that a CDF shows the cumulative probability of a random variable being less than or equal to a given value, while a PDF shows the relative likelihood of a random variable taking on a specific value.
CDFs are often used to determine the probability of a random variable being within a certain range or above/below a certain value. PDFs, on the other hand, are often used to determine the likelihood of a random variable taking on a specific value.
No, a CDF and a PDF cannot be used interchangeably. They represent different aspects of a probability distribution and have different mathematical properties. However, they are related and can be used together to fully describe a probability distribution.