How Many Types Of Random Variables Are Available?

There are two types of Random variables they are discrete and continuous random variables

The rule that gives each result in a sample space a numerical value is known as a random variable. They can be discrete or continuous, depending on the random variable. A random variable is deemed discrete if it only accepts certain values within a given range. It is ongoing in all other cases. Typically, we use capital letters to designate the random variables, such as X and Y. It is said that X has a discrete random variable when X has values 1, 2, 3,...

In order to give probabilities to a collection of potential values, a random variable must be measured as a function. It is evident that some physical elements that are unpredictable affect the outcomes. For example, whether a fair coin lands heads or tails will depend on any conceivable physical circumstances. Which result will be recorded is impossible to foresee. Although there are other possibilities, such as the coin breaking or getting lost, these are not taken into account.

Variate

A generalisation of the random variable is referred to as a variate. It shares the same characteristics of random variables without emphasising a specific kind of probabilistic experiment. It consistently abides by a certain probability law.

• When a variate cannot assume every value in the given range, it is referred to as a discrete variate.

• A continuous variate is one that can take on any of the specified numerical values across the whole range.

Types Of Random Variables

In the beginning, it was mentioned that there are two random variables, like:

• Discrete Random Variable

• Continuous Random Variable

Discrete Random Variable

Only a finite number of different values, including 0, 1, 2, 3, 4,..., and so on, are possible for a discrete random variable. The probability mass function, which compares a set of probabilities with each of a random variable's potential values, is part of the probability distribution of the random variable.

Continuous Random Variable

If a numerically valued variable can take on the values a and b at any time and in any unit of measurement, it is said to be continuous. It is referred to as a continuous random variable if the random variable X is capable of taking on an unlimited and uncountable range of values. It is claimed that X is a continuous random variable in the interval (a, b) if it can take any value within that range.

Examples Of Random Variable Usage In Real Life Situations

• The number of car accidents that take place in a certain city on a given day is an example of a discrete random variable.

• The marathon time of a certain runner is an illustration of a continuous random variable.

• The interest rate on loans in a particular nation is an illustration of a continuous random variable.

• The amount of merchandise sold at a store on a certain day is an example of a discrete random variable.