A continuous random variable is a type of random variable that can take on any value within a certain range. Unlike a discrete random variable, which can only take on specific, isolated values, a continuous random variable can take on an infinite number of values within a given interval.
A discrete random variable can only take on specific, isolated values, while a continuous random variable can take on any value within a given interval. This means that a continuous random variable is measured on a continuous scale, while a discrete random variable is measured on a discrete scale.
The probability density function (PDF) of a continuous random variable is a function that describes the probability of the variable taking on a particular value. It is represented by a curve on a graph, and the area under the curve between two points represents the probability of the variable falling within that range.
The probability of a continuous random variable falling within a certain range is calculated by finding the area under the probability density curve between the two points that define the range. This can be done using calculus by taking the integral of the probability density function.
Some examples of continuous random variables include height, weight, temperature, and time. These variables can take on an infinite number of values within a certain range and are measured on a continuous scale.