. . Random variable Introduction: Let the random experiment be the toss of a coin. When ‘ n ’ coins are tossed, one may be interested in knowing the number of heads obtained.
When a pair of dice is thrown, one may seek information about the sum of sample points. Thus, we associate a real number with each outcome of an experiment. In other words, we are considering a function whose domain is the set of possible outcomes and whose range is subset of the set of real numbers. Such a function is called random variable .
In algebra, you learned about different variables like X or Y or any other letter in a particular problem. Thus in basic mathematics, a variable is an alphabetical character that represents an unknown number. A random variable is a variable that is subject to randomness, which means it could take on different values. In statistics, it is quite general to use X to denote a random variable and it takes on different values depending on the situation.
Some of the examples of random variable: (i) Number of heads, if a coin is tossed times. (ii) The return on an investment in one-year period. (iii) Faces on rolling a die. (iv) Number of customers who arrive at a bank in the regular interval of one hour between .
a.m and . p.m from Monday to Friday. (v) The sale volume of a store on a particular day. For instance, the random experiment ‘ E ’ consists of three tosses of a coin and the outcomes of this experiment forms the sample space is ‘ S ’.
Let X denotes the number of heads obtained. Tossing a Coin Fig. . Here X is a real number connected with the outcome of a random experiment E .
The details given below Outcome (ω) Values of (HHH) (HHT) (HTH) (THH) Outcome (ω) Values of (HTT) (THT) (TTH) (TTT) i.e., R X = { , , , } From the above said example, for each outcomes ω, there corresponds real number X (ω). Since the points of the sample space