CE 29 Discrete Probability Distributions - Module 3 Terminologies

Modeling the number of successes in a fixed number of independent Bernoulli trials (e.g., number of heads in 10 coin flips).

Binomial distribution

Modeling a single trial with two possible outcomes: success (1) or failure (0) (e.g., a single coin flip).

Bernoulli distribution

Modeling the number of trials needed to achieve the first success in repeated Bernoulli trials (e.g., number of attempts until the first heads).

Geometric distribution

Modeling the number of trials needed to achieve a specified number of successes (e.g., number of attempts until 3 heads).

Negative Binomial distribution

Modeling the number of events occurring in a fixed interval of time or space (e.g., number of emails received in an hour).

Poisson distribution

Modeling scenarios where each outcome in a finite set is equally likely (e.g., rolling a fair die).

Discrete Uniform distribution

Modeling outcomes of experiments with more than two categories and multiple trials (e.g., rolling a die multiple times).

Multinomial distribution

Modeling the number of successes in a sample drawn without replacement from a finite population (e.g., drawing defective items from a batch).

Hypergeometric distribution

It means the probability of success remains the same for each trial, regardless of past outcomes. Starting the count of trials at any point doesn’t change the distribution (e.g., the chance of success on the 5th trial is the same as on the 1st).

Lack of Memory Property

The outcome of one trial doesn’t affect the outcome of another, and the probability of success is the same for every trial. Therefore:

trials in a geometric distribution considered independent