A random variable is a variable that contains the outcomes of a chance experiment. A random variable is a discrete random variable if the set of all possible values is at most a finite or a count ably infinite number of possible values. In most statistical situations, discrete random variables produce values that are non-negative whole number. The battery experiment produces a distribution that has discrete outcomes. Any one trial of the experiment will contain 0, 1, 2, or 3 defective batteries. It is not possible to get 1.58 defective batteries. It could be said that discrete random variables are usually generated from experiments in which things are “counted” not “measured”.
Continuous random variables take on values at every point over a given interval. Thus continuous random variables have no gaps or unassumed values. It could be said that continuous random variables are generated from experiment in which things are “measured” not “counted.”
Once continuous data are measured and recorded, they become discrete data because the data are rounded off to a discrete number. Thus in actual practice, virtually all business data are discrete. However, for practical reasons, data analysis is facilitated greatly by using continuous distributions on data that were continuous originally. The outcomes for random variables and their associated probabilities can be organized into distributions. The two types of distributions are discrete distribution, constructed from discrete random variables, and continuous distributions, based on continuous random variables.
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