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
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 random variable
Say x is a variable, which can take a finite number of values in an interval of the domain, is called a discrete random variable. For 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).
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.
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 X 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, X + Y, X -Y, aX, bY or aX + by are also random variables where a and b are any two constants except that a and b both are not zero.