 # Random Variable

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What is a Random Variable?

A random variable is a variable that denotes the outcomes of a chance experiment. For example, suppose an experiment is to measure the arrivals of cars at a tollbooth during a minute period. The possible outcomes are: 0 cars, 1 car, 2 cars, …, n cars.

There are two categories of random variables

(1) Discrete random variable

(2) Continuous random variable.

### Discrete Random Variable

A discrete random variable is one in which the set of all possible values is at most a finite or a countably infinite number. (Countably infinite means that all possible value of the random variable can be listed in some order).

Some examples of experiments that yield discrete random variables are:

1. Randomly selecting 30 people who consume soft drinks and determining how many people prefer diet soft drinks.

2. Determining the number of defective items in a batch of 100 items.

3. Counting the number of people who arrive at a store in a ten-minute interval.

### Continuous Random Variable

A continuous random variable takes on any value in a given interval. So, continuous random variables have no gaps. Continuous random variables are usually generated from experiments in which things are “measured” not “counted”.

Some examples of experiments that yield continuous random variables are:

1. Sampling the volume of liquid nitrogen in a storage tank.

2. Measuring the time between customer arrivals at a store.

3. Measuring the lengths of cars produced in factory.

The outcomes for random variables and their associated probabilities can be organized into distributions. The two types of distributions are discrete distributions, which describe discrete random variables, and continuous distributions, which describe continuous random variables. Discrete distributions include the binomial distributions, Poisson distribution and hypergeometric distribution. Continuous distributions include the normal distribution, uniform distribution, exponential distribution, t distribution, chi-square distribution and F distribution.

Understanding Random Variables - Probability Distributions
The idea of a random variable can be surprisingly difficult. In this video we help you learn what a random variable is, and the difference between discrete and continuous random variables. Introduction to random variables and probability distribution functions Random variables - Probability and Statistics
Basic idea and definitions of random variables Discrete and continuous random variables
Defining discrete and continuous random variables. Working through examples of both discrete and continuous random variables.

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