11.2 Random Variable

. Random Variable The outcome from a random experiment is not always a simple thing to represent in notion. In many random experiments that we have considered, the sample space S has been a description of possible outcomes. That is the outcome of an experiment, or the points in the sample space S , need not be numbers.

For example in the random experiment of tossing a coin, the outcomes are H (head) or T (tail). It is necessary to deal with numerical values, in some situation, for outcomes of random experiment. Therefore, we assign a number to each outcome of the experiment say 1to head and to tail. Such an assignment of numerical values to the elements in S is called a random variable .

A random variable is a function . Thus, a random variable is: Definition . A random variable X is a function defined on a sample space S into the real numbers  such that the inverse image of points or subset or interval of  is an event in S , for which probability is assigned. We use the capital letters of the alphabet, such as X, Y, and Z to represent the random variables and the small letters, such as x, y, and z to represent the possible values of the random variables.