Discrete Distributions

A discrete distribution describes outcomes that can be counted, such as the roll of a die or the number of customers who visit a shop in a day. The possible values are separate, with gaps between them, and each one has its own probability. Together, these probabilities add up to 1.

The Discrete Uniform Distribution

  • The discrete uniform distribution describes a set of countable outcomes that are all equally likely. If there are n possible outcomes, each one has a probability of 1 divided by n.

  • Rolling a single fair die is the simplest example: there are six possible outcomes, so each number from 1 to 6 has a probability of 1/6. Drawn as a chart, the distribution appears as a row of bars that are all the same height.

The Bernoulli distribution

  • The Bernoulli distribution describes a single event with only two possible outcomes, usually labelled success and failure. The probability of success is written as p, so the probability of failure is 1 minus p.

  • For example, if a customer has a 0.3 probability of making a purchase, the probability that they do not is 0.7. A single coin flip is the simplest case, with p = 0.5 for heads.

The Binomial Distribution

  • The binomial distribution counts the number of successes across a fixed number of independent Bernoulli events. In other words, it repeats the same yes-or-no event several times and asks how many successes occur.

  • For example, if each customer has a 0.3 probability of making a purchase, the binomial distribution gives the probability that exactly 3 of 10 customers make a purchase. The most likely result is 3, since 30% of 10 is 3, while results far from 3, such as 0 or 10, are much less likely.

The Poisson Distribution

  • The Poisson distribution counts how many times an event happens within a fixed period of time or space. It is described by a single number, the average rate at which the event occurs.

  • For example, if a website receives an average of 4 visits per minute, the Poisson distribution gives the probability of receiving exactly 0, 1, 2 or any other number of visits in a given minute.

    • The most likely results are close to 4, while much higher counts, such as 12 visits in one minute, are rare. Unlike the binomial distribution, there is no fixed number of tries: the count has no set upper limit.

Connect with Me!

LinkedIn: caroline-rennier

Email: caroline@rennier.com