A Probability Density Function (PDF) is a mathematical function that describes the probability of a continuous random variable falling within a certain range of values. It is used to analyze and understand the distribution of data.
A PDF gives the probability of a random variable taking on a specific value, while a CDF gives the probability of the random variable being less than or equal to a certain value. In other words, a PDF shows the probability of a single outcome, while a CDF shows the probability of a range of outcomes.
The area under a PDF curve represents the probability of the random variable falling within a certain range of values. The total area under the curve is always equal to 1, as the probability of any outcome occurring is always 100%.
A PDF is used in data analysis to understand the distribution of a dataset and to make predictions about future outcomes. It can also be used to compare different datasets and identify any similarities or differences in their distributions.
The assumptions of a Probability Density Function are that the data is continuous, the total area under the curve is equal to 1, and the probability of any particular outcome is between 0 and 1. Additionally, the PDF assumes that the data is normally distributed, meaning it follows a bell-shaped curve.