Continuous Probability Distribution versus Discrete Probability Distribution

From Computational Statistics (CSE383M and CS395T)
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Discrete probability distributions comes into play when there are a finite number of discrete possible events. You can assign a probability to the discrete events and the sum of the probability of all the events must be 1. A standard example is the roll of a dice. The variable (dice roll) takes on certain values. There are six possible events/outcomes, each of the numbers 1 through 6. Assuming a fair dice, each of the numbers are equally likely. Rolling the number 2 takes a probability of <math>\frac{1}{6}</math>.

Continuous probability distributions have an infinite set of events, and therefore different from discrete probability distributions in that a single event has zero probability. If you pick one, you have an infinite number left. The probabilities come into play when you are looking at an interval. A probability density function is needed to determine the actual probabilities of intervals. An example is height versus the percentage of people. The height distribution looks like a normal distribution.