#### Random Variable and its types with properties

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In statistics, A Random Variable is a set of possible values from a random experiment which is known in advance and the experiment can be repeated underer identical condition. According to Investopedia,

“A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment’s outcomes.”

A random experiment is an experiment in which

• All possible outcomes of the experiment are known in advance.
• Any performance of the experiment results in an outcome that is not exactly known in advance.
• The experiment can be repeated under identical condition.

More precisely we can say that,

There is a rule that assigns a real number to each outcome (sample point) of a random experiment is called a random variable (r.v.). It is governed by a function of the variable. Hence, a it is a real-valued function X (x) of the elements of the simple space (omega) where x is an element of (omega). Further, the range of the variable will be a set of real values.

For example

In tossing a coin, x =1, if the coin falls with head, and x= 0 if the coin falls with a tail. The height of persons can be given by X (x)= X, the height is measured in centimetres or inches. A random variable is usually denoted by any of the capital Latin letters X, Y, Z, U, V etc.

### Different types of random variables

Generally, there are two types, namely

• Discrete
• Continuous

### Discrete random variable

Say x is a variable, which can take a finite number of values in an interval of the domain, is called discrete random variableFor example, if we toss a coin, the variable can take only two values 0 and 1 assigned to tail and head respectively, i.e.,

X(x)= 0(if x is tail) or 1(if x is head).

### Continuous

Let, A variable X, which can take any value in its domain or in an interval or the union of intervals on the real line, is called Continuous random variable. For a conti­nuous variable, the probability of a point is zero, i.e., P (X = x) =0.

### Properties of random variable

The properties are following,

• If X is a variable and a,b are any two constants, aX + b is also a random variable.
• If is a variable, X square is also a variable.
• If X is a variable, 1/X is also a variable.
• If X and Y are two variables defined over the same space, Y, X -Y, aX, bY or aby are also random variables where and b are any two constants except that and b both are not zero.

### Releated

#### Data Levels of Measurement (Nominal, Ordinal, Interval, Ratio) in Statistics

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Spread the love          Data levels in statistics indicates the measurement levels in statistics. In statistics, the statistical data whether qualitative or quantitative, are generated or obtain through some measurement or some observational process. Measurement is essentially the task of assigning numbers to observations according to certain rules. The way in which the numbers are assigned to […]

#### Correlation Analysis definition, formula and step by step procedure

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Spread the love          The relationship between two or more random variables are generally defined as the correlation. It is the major part of bivariate analysis. When variables are found to be related, we often want to know how close the relationship is. The study of the relationship is known as correlation analysis. The primary objective of […]