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Random Variable is a very important topic of statistics. A variable value is determined by the result of a random experimentation is termed as random variable. This is known as chance variable or stochastic variable. A random variable may be separate or continuous. If it has integer values such as 0, 1, 2, 3, 4, and so on then it is known as a discrete Random Variable. Various examples of discrete random variables are number of printing errors in each page of a book, the number of telephone calls done by the telephone operator of a firm. If the random gets all values, at a certain interval of time, then the random variable is referred as a nonstop random variable. For example: the quantity of rainfall in a rainy season, the height and weight of individuals etc.
In symbolic terms, if a variable Y can suppose discrete set of values Y1, Y2……Yk by respective probabilities P1, P2 ….. Pk where P1 + P2 + … Pk = 1, we affirm that a discrete probability distribution of Y has been defined. The function P(Y) which has the applicable values P1, P2 … for Y = Y1, Y2 ….. Yk is known as the probability function or frequency function of X.
It should be important that a probability distribution is same as relative frequency distribution through probabilities replacing relative frequencies. Consequently we can think of probability distributions as theoretical or ideal restrictive forms of relative frequency distribution when the quantity of observations made is very large. For this cause, we can think of probability distributions as distributions for populations, whereas relative frequency distributions are distributions taken from this population.