Random Variable, Types and Applications
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Random Variable
A random variable is a variable that takes on different values based on the outcomes of a random phenomenon. It can be thought of as a function that assigns numerical values to the outcomes of a random process.
For Example: When we roll a fair six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6. Each of these outcomes is equally likely. Let's define a random variable X that represents the outcome of rolling the die. Here, X can take any one of the values 1, 2, 3, 4, 5, or 6. In this case, X is a discrete random variable because it can only take on a finite number of specific values.
Types of Random Variables:
Discrete Random Variables: A discrete random variable can only take specific, separate values. For example, let X represent the number of heads obtained in three flips of a fair coin. The possible values of X are 0, 1, 2, and 3.
Continuous Random Variables: A continuous random variable can take any value within a given range. For instance, let Y represent the exact height of students in a class, measured in meters. Y can take any value within a realistic range, such as 1.5 to 2.0 meters.
