The geometric distribution is the probability distribution used to represent the chances of experiencing a certain number of failures before encountering the first success of an event. The events follow a similar pattern as followed by the Bernoulli trials, i.e., the experiment has success and failure as the only two possible outcomes. The mean represents the average value that one can expect as the outcome of an experiment that is repeated a number of times. The mode of the data corresponds to the value that has the highest chances of occurrence. The variance is the measure of the spread of data. Median is another method of determining central tendency, which is generally preferred when the distribution includes eccentric data, i.e., there exist specifically large and small values. Usually, it is feasible to calculate the mean, mode, and variance of the geometrically distributed data; however, calculation of median is not possible because the data is not eccentric and only consists of two outcomes either success or failure.
Examples of Geometric Distribution
1. Cost-Benefit Analysis
Most organisations frequently make use of geometric probability distribution to perform a cost-benefit analysis. The purpose of cost-benefit analysis is to estimate the financial benefit that the organisation would gain upon making a certain decision or action while subtracting the cost of implementation of that particular decision or action. This helps improve the decision-making ability of the organisation and reduces the chances of loss of capital.
2. Sports Applications
The geometric distribution is used in a number of sports such as basketball, baseball, etc. The probability that a batter is able to make a successful hit before three strikes can be estimated efficiently with the help of a geometric probability distribution function. Here, the batter earning a hit is considered as the success of the event, while the batter missing the ball is considered to be a failure.
3. Tossing a Coin
Tossing a coin is one of the best examples of the experiments that follow Bernoulli trials. Let us assume that obtaining heads on the top of the coin when it is tossed is considered a success while obtaining tails on the top is considered a failure. The probability of the number of times a coin is required to be tossed to get heads on its top can be represented easily with the help of geometric distribution.
4. Feedback from Customers
The geometric distribution is used to calculate an approximate number of customers that may give positive or negative feedback regarding a particular product. For instance, if a manager conducts a survey regarding the food quality of his/her restaurant, the probability that he/she gets positive feedback after receiving negative comments from ten people can be estimated in advance. Here, the positive feedback acts as a success of the event, while the negative comments lead to the failure of the experiment. This helps the person to draft an appropriate response to the consumers with negative feedback and improve sales.
5. Number of Supporters of a Law
The geometric distribution is generally used to compute the probability of success or failure of establishing a new law into action in advance. If the probability of a person supporting a certain law recently imposed by the government is known, then the geometric probability distribution can be used to estimate the number of people present at a particular conference who would be in support of the law and the number of people who would be against it. This helps the politicians and people in charge to draft their speeches accordingly.
6. Number of Faulty Products Manufactured at an Industry
The geometric probability distribution is highly used in quality control departments of the industry. When a product is manufactured in bulk quantity, naturally some of the products are found to be faulty. The probability that a faulty product is found after reviewing fifty non-faulty products can be calculated with the help of geometric distribution. It helps the quality control managers to speed up the process of reviewing the manufactured products before shipping them to their destination.
7. Number of Bugs in a Code
When a programmer runs a particular code, a certain number of bugs are expected to occur. If the probability of a bug occurring in a code is known, then the probability of the code running successfully after compiling it a certain number of times can be calculated with the help of geometric probability distribution. This helps to estimate the approximate time required by the developer to complete a particular project.
8. A Teacher Examining Test Records
Let us suppose a teacher is going through the test records of his/her students. The probability that an ‘A’ graded test appears after he/she examines at least twenty tests can be easily calculated with the help of geometric distribution. This helps the teacher to keep a track record of the performance of the students and to improve it.
9. Playing a Game
While playing a particular game, there are basically two possible chances, i.e., either you win the game or you lose it. The probability that one has to suffer a total of ten losses before experiencing a win can be calculated with the help of geometric distribution. Hence, it forms a prominent example of geometric distribution in real life.
10. Throwing Darts at a Dartboard
Throwing a dart at a dartboard is yet another example of geometric distribution in real life. The player tends to throw the dart at the board and aims for the centre of the board. The chances that a minimum of twelve darts are thrown towards the board before one of them hits the centre are usually calculated with the help of geometric probability distribution. This means that one can easily evaluate the chances of hitting a bullseye in advance.
11. Number of Network Failures
The geometric distribution is used by a number of telecommunication and broadcasting companies to improve their customer satisfaction index. Let the probability of network failure occurring in a particular locality is equal to 0.3, then the probability that a customer who does not have any network-related issue is obtained after obtaining feedback from ten different customers can be calculated easily with the help of geometric distribution. This helps the organisation to form and implement the necessary steps required to improve network connectivity in a particular area.