Theory Of Probability- Random Variable

Theory Of Probability- Random Variable [ A random variable is a fundamental concept in the theory of probability and statistics. It is a mathematical abstraction that represents an uncertain or random quantity or outcome in a probabilistic experiment or process. In simpler terms, it's a way to assign numerical values to the possible outcomes of a random event. There are two main types of random variables: Discrete Random Variable: A discrete random variable can take on a countable number of distinct values, often represented by integers. Examples include the number of heads when flipping a coin multiple times or the outcome of rolling a six-sided die. Continuous Random Variable: A continuous random variable can take on any value within a certain range or interval. It typically represents measurements that can have an infinite number of possible outcomes, such as the height of individuals or the time it takes for a process to complete. Random variables are a crucial part of probability theory because they allow us to describe and analyze uncertainty and randomness in a mathematical and quantitative way. Probability distributions, such as the probability mass function for discrete random variables or the probability density function for continuous random variables, help us understand the likelihood of different outcomes occurring. Random variables play a central role in various statistical techniques, including hypothesis testing, regression analysis, and probability modeling, making them a fundamental concept in the field of statistics.] [PPT made by Chaitali Uke]