- Probability Distributions
The binomial distribution is used in situations that have only two possible outcomes, hence the name “binomial.” The outcome is dichotomous. There are four common requirements for a binomial distribution. Firstly, the number of trials has to be fixed. The number of trials must be clearly defined, and there must not be any variations, and it cannot be altered during the analysis. The process of each trial should be the same for all the trials, even if there might be a variation in the outcomes. The number of trials is denoted as n.
Secondly, the trials have to be independent. A trial should not have any effect on the other trials.
Thirdly, there have to be two different classifications. This can either be a success, p or failure, q. in that, p+q=1. Finally, all the trials must have the same probability of success all the process of investigation.
The binomial distribution can be used in determining the number of patients reacting to a certain medication. For example, if a researcher discovers a new therapy for cancer patients. Thus, for each patient who uses the treatment, the outcome would be either a success or failure. If a patient responds positively, then it is a success. However, if the response if negative, then it is a failure.
The geometric distribution is model is used in situations where there is a need to determine the number of attempts required to achieve success. It is the number of failures obtained before the first success is achieved. It is used in population modeling and return of investment research. Geometric distribution has three main requirements. First, is the trials can be one or more, and each trial is a failure except the last one that has to be a success. Secondly, there has at least one trial for success as the trials are repeated. Thirdly, all the trials must have the same probability of success and an equal likelihood of failure. The trials have to be independent of each other.
An example of geometric distribution would in a retail store where the store manager would want to determine the number of customers who come to store until one customer buys something. Thus, the geometric distribution would show the number of customers who entered the store and did not make the purchase until the first customer to make a purchase is found. Hence there are various failures be the first success is achieved.
Poisson distribution is the probability of several events taking place in a specified time frame. Poisson distribution has four main conditions. First, the number of times in which an even can occur within a specified period is not limited. Secondly, the events have to occur independently. One event occurring does not affect the other event’s probability of occurring. Additionally, the frequency of occurrence has been constant. Finally, an event’s likelihood of occurring is affected by the length of the period.
Poisson distribution can be used to analyze the various events that determine the number of customers who drive-through a fast-food restaurant. It can be sued to determine the probability of 0 customers coming to the restaurant (lull activity) and the likelihood of the number of customers being more than average (flurry activity). This information can be used to manage the events and ensure the staffing and scheduling support both the lull and flurry activities.
There are similarities and differences between the three probability distributions. They are all discrete and measure random events. Similarly, their events are all independent, with each event having the same probability of success and the equal probability of failure.
However, the binomial and geometric distribution is used on discrete events, while Poisson is used on continuous events. Similarly, binomial, two possible outcomes are expected. On the other hand, in geometric, the number of failures required before the first success is determined. Finally, in Poisson, the number of events the take place in a specified time frame is determined.