**Introduction**

Probability is one of the easiest and favorite chapters for most students. Letâ€™s take a simple example of tossing a coin, so the probability of getting head and tail is equal. Here the prediction variable that we are using to estimate the coin toss probability is called â€śRandom Variableâ€ť.

Another popular example is rolling dice, and here all six sides have equal probability, so the estimator we are using to predict the possible outcomes is called Random Variables.

- A Random Variable is a set of possible values from a random experiment.
- The set of possible values is called the Sample Space.
- A Random Variable is given a capital letter, such as X or Z.
- Random Variables can be discrete or continuous.

**Types of Random Variables**

There are three types of random variables:

- Discrete random variables
- Continuous random variables
- Mixed random variables

**1.Discrete Random Variables:**

Discrete random variables are random variables whose range is a countable set. A countable set can be either a finite set or a countably infinite setâ€”for example, shoe size or weight of student.

**2. Continuous Random Variables:**

Continuous random variables, on the contrary, have a range in the forms of some interval, bounded or unbounded, of the real line. For example, Height, weight, temperature, and length are all examples of continuous data. Some continuous data will change over time; the weight of a baby in its first year or the temperature in a room throughout the day.

**3. Mixed Random Variables:**

Mixed random variables are a mixture of both continuous and discrete variables. These variables are more complicated than the other two. For example, the number of owl eggs in a nest, the number of times a college student changes major, shoe size, weight of a student.

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**Applications of Random Variables**

- Random variables are used in all engineering domains in Civil to calculate the beam length.
- Random variables are used in Machine learning and neural networks.
- In General Random Variables, are used for tossing a coin, rolling a dice.
- Random variables are used for statistical analysis.
- Random variables are used to check whether a circuit accepts data or not in electrical engineering.
- Random variables are used for the emergency landing of planes.