# Random Variable in Statistics: A Quick Review Notes (2024)

### Introduction to a Random Variable in Statistics

A random variable in statistics is a variable whose value depends on the outcome of a probability experiment. As in algebra, random variables are represented by letters such as $X$, $Y$, and $Z$. A random variable in statistics is a variable whose value is determined by chance. A random variable is a function that maps outcomes to numbers. Read more about random variables in Statistics: Random Variable.

### Random Variable in Statistics: Some Examples

• T = the number of tails when a coin is flipped 3 times.
• s = the sum of the values showing when two dice are rolled.
• h = the height of a woman chosen at random from a group.
• V = the liquid volume of soda in a can marked 12 oz.
• W = The weight of an infant chosen at random in a hospital.

### Key Characteristics of a Random Variable

• Randomness: The value of a random variable is determined by chance.
• Numerical: It assigns numbers to outcomes.
• Function: It is technically a function that maps outcomes to numbers.

### Types of Random Variables

There are two basic types of random variables.

Discrete Random Variables: A discrete random variable can take on only a countable number of values. It can have a finite or countable number of possible values.

Continuous Random Variables: A continuous random variable Can take on any value within a specified interval. It can take on any value in some interval.

Examples of Discrete and Continuous Random Variables

• The variables $T$ and $s$ from above are discrete random variables
• The variables $h$, $V$, and $W$ from above are continuous random variables.

### Importance of Random Variables in Statistics

Random variables are fundamental to statistics. Random variables allow us to:

• Use mathematical tools to analyze uncertain events.
• Model the real-world phenomena.
• Calculate probabilities of events.
• Compute expected values and variances.
• Make statistical inferences.

Random variables form the basis for probability distributions and are fundamental to statistical inference. Random variables provide a bridge between the real world of uncertainty and the mathematical world of probability.

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