Statistical Methods

Unit 2 - Probability distributions

2.1.Introduction
In real life situation we always infer about a population on the basis of a sample study. For a given frequency distribution of a variable in the sample under study, we can get relative frequencies which are probabilities of occurrence of different values of random variables. Probability distribution is analogous to a relative frequency distribution with probabilities replacing relative frequencies. Thus, probability distributions can be regarded as theoretical or limiting forms of relative frequency distributions, when the number of observations made is very large. Hence, probability distributions can be considered as distributions, of populations, whereas relative frequency distributions are distributions of samples drawn from these populations. Frequency distributions which arise in sample can be approximated by well known theoretical probability distributions which serve as useful tools in making inferences and decisions under conditions of uncertainty on the basis of limited data or theoretical considerations.