Continuous random variables can take any value within a range. Unlike discrete variables, they include fractional and decimal values. These variables are often modeled using probability distributions.

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

The reports aim to provide a clear understanding of key concepts in probability and statistics, making them accessible to learners at all levels. Each report breaks down complex topics into digestible ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

Roll a die and ask students to identify the random variable. Since a die can only take on values of 1, 2, 3, 4, 5, or 6, this is a discrete random variable. Repeat ...