A random variable is a numerical quantity whose value is determined by chance or probability. It can take on different values in a given situation, and its properties can be described by a probability distribution.
A discrete random variable can only take on specific, separate values, while a continuous random variable can take on any value within a certain range. For example, the number of children in a family is a discrete random variable, while the height of a person is a continuous random variable.
A random variable is used to model the outcomes of a random experiment, and its probability distribution describes the likelihood of each possible outcome. It allows us to calculate the probability of specific events occurring based on the values of the random variable.
The expected value of a random variable is the weighted average of all the possible values it can take on, where the weights are given by their respective probabilities. It represents the theoretical average of a large number of repetitions of the random experiment.
Random variables are used in statistical analysis to model and analyze data that is subject to chance or uncertainty. They help us understand and make predictions about real-world phenomena, and are commonly used in fields such as economics, physics, and psychology.