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Poisson distribution is a distribution function used to characterize a phenomenon with extremely low chances of happening within a given definite period or space. This function was developed in the 1830s by revered French mathematician Simeon-Denis Poisson. He hoped this function would explain the number of times a player would win a probability game that is rarely won even in a large number of attempts.
Probability outcomes that are judged to be equipossible can be assigned equal probabilities. This concept is what we call equiprobability. Laplace's principle of indifference states that the researcher is justified to assign the probability 1/N in cases where there is no information that n number of mutually exclusive phenomena can occur. This concept is usually applied in situations such as lotteries, dice rolling, and other experiments that have symmetry structures.
In conditional probability, the likelihood of an event happening depends on some association to one or multiple other events. For example, in a scenario where it is raining but you still need to go out, a conditional probability will evaluate these two events while considering that they are related.
A binomial distribution is the likelihood of an experiment or survey carried out multiple times resulting in success or failure. The prefix "bi" usually means two. So we can say that binomial distribution means that we can only expect two possible outcomes. For example. If we toss a coin, we can only expect a head or a tail. Similarly, if you take a test, you can only pass or fail. In the binomial formula:
- The first variable n represents the number of times the experiment will be conducted
- The probability of a single specific outcome is represented by the second variable, p.