A continuous random variable is a variable that can take on any numerical value within a given range. Unlike a discrete random variable, which can only take on specific, separate values, a continuous random variable can take on an infinite number of values within a range.
A continuous random variable is different from a discrete random variable in that it can take on an infinite number of values within a range, while a discrete random variable can only take on specific, separate values. Additionally, the probability distribution of a continuous random variable is described by a probability density function, while the probability distribution of a discrete random variable is described by a probability mass 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 given range, and are not limited to specific, separate values.
A continuous random variable is typically represented by the letter X, and its probability distribution is described by a probability density function (PDF). The PDF represents the relative likelihood of different values of the continuous random variable occurring, and the area under the curve of the PDF must equal 1.
The probability of a continuous random variable is calculated by finding the area under the curve of the probability density function (PDF) within a given range. This can be done using integrals in calculus. The probability of a continuous random variable taking on a specific value is always equal to 0, as the area under a single point on the PDF is infinitesimally small.