Continuous Random Variables

Continuous random variables are random variables that can take on any value within a certain range or interval. They are represented by continuous probability density functions (PDFs) rather than discrete probability mass functions (PMFs).

Examples of continuous random variables include height, weight, temperature, and time. These variables can take on any value within a certain range, such as 0 to infinity for weight or -273.15 to infinity for temperature.

The probability of a continuous random variable taking on a specific value is zero, as there are an infinite number of possible values. Instead, the probability is represented by the area under the PDF curve between two points on the interval. The total area under the curve is equal to 1, representing the total probability of all possible values within the interval.

Continuous random variables are used in many fields, including physics, engineering, and finance. They are often modeled using various probability distributions, such as the normal distribution, the exponential distribution, or the uniform distribution.