Probability and Sampling Distributions

When an experiment is conducted, such as tossing coins, rolling a die, sampling for estimating the proportion of defective units, several outcomes or events occur with certain probabilities. These events or outcomes may be regarded as a variable which takes different values and each value is associated with a probability. The values of this variable depends on chance or probability. Such a variable is called a random variable. Random variables which take a finite number of values or to be more specific those which do not take all values in any particular range are called discrete random variables. For example, when 20 coins are tossed, the number of heads obtained is a discrete random variable and it takes values 0,1,...,20. These are finite number of values and in this range, the variable does not take values such as 2.8, 5.7 or any number other than a whole number. In contrast to discrete variable, a variable is continuous if it can assume all values of a continuous scale. Measurements of time, length and temperature are on a continuous scale and these may be regarded as examples of continuous variables. A basic difference between these two types of variables is that for a discrete variable, the probability of it taking any particular value is defined. For continuous variable, the probability is defined only for an interval or range. The frequency distribution of a discrete random variable is graphically represented as a histogram, and the areas of the rectangles are proportional to the class frequencies. In continuous variable, the frequency distribution is represented as a smooth curve.