Question

Think about these three probability distributions: hypergeometric, binomial, and Poisson and describe one or more ways that you might use any of these distributions to explore their applications in different situations that need not be particularly economically valuable

Answer 1

Hypergeometric Distribution: In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of {\displaystyle k} successes (random draws for which the object drawn has a specified feature) in {\displaystyle n} draws, without replacement, from a finite population of size {\displaystyle N} that contains exactly {\displaystyle K} objects with that feature, wherein each draw is either a success or a failure.

Application: A small voting district has 101 female voters and 95 male voters. A random sample of 10 voters is drawn.

Binomial Distribution: In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q = 1 − p).

Application: Let’s say that 80% of all business startups in the IT industry report that they generate a profit in their first year. If a sample of 10 new IT business startups is selected, find the probability that exactly seven will generate a profit in their first year.

Poisson Distribution: The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period.

Application: A Poisson distribution can be used to analyze the probability of various events regarding how many customers go through the drive-through. It can allow one to calculate the probability of a lull in activity (when there are 0 customers coming to the drive-through) as well as the probability of a flurry of activity (when there are 5 or more customers coming to the drive-through). This information can, in turn, help a manager plan for these events with staffing and scheduling.