Definition Of Random Variable Math

Definition of random variable the concept of random variable is a natural extension of the concept of a random experiment.

Definition of random variable math. A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment s outcomes. However convergence issues associated with the infinite sum necessitate a more careful definition. A random variable is a variable that is subject to random variations so that it can take on multiple different values each with an associated probability. There are two main classes of random variables that we will consider in this course.

Similarly two random variables are independent if the realization of one does not affect the probability distribution of the other. Intuitively the expectation of a random variable taking values in a countable set of outcomes is defined analogously as the weighted sum of the outcome values where the weights correspond to the probabilities of realizing that value. Let s give them the values heads 0 and tails 1 and we have a random variable x. Some natural examples of random variables come from gambling and lotteries.

We could get heads or tails. A random variable could be discrete such as in the result of rolling a six sided die. This week we ll learn discrete random variables that take finite or countable number of values. Two events are independent statistically independent or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

Independence is a fundamental notion in probability theory as in statistics and the theory of stochastic processes. Random variables are really ways to map outcomes of random processes to numbers. When dealing with collections of more than two events a weak and a strong notio. A random variable is a set of possible values from a random experiment.

So if you have a random process like you re flipping a coin or you re rolling dice or you are measuring the rain that might fall tomorrow so random process you re really just mapping outcomes of that to numbers. Random variables are often designated by letters and can be classified. Random variable denotes a value that depends on the result of some random experiment. Let s recall for that a random experiment is simply a procedure that leads to a non deterministic outcome meaning we cannot predict it beforehand.