Statistics: Probability Distributions (An Overview)

Rahul S
6 min readSep 5, 2023

Random Variable: All possible outcomes of a random experiment are random variables. A random variable set is denoted by X.

Discrete Distributions

Bernoulli Distribution

We have a single trial (only one observation) and 2 possible outcomes. For example, flipping a coin. Let’s say we accept True for heads. Then if the probability of getting heads is p, the probability of the opposite situation is 1-p.

Binomial Distribution

Bernoulli was for a single observation. More than one Bernoulli observations create a binomial distribution. For example, tossing a coin several times in a row.

Trials are independent of each other. The result of one attempt does not affect the next.

The binomial distribution can be expressed as B(n, p ). n is the number of trials and p is the probability of success.

The distribution shows an increased probability of an increase in the number of successful outcomes.

p: the probability of success,
n: number of trials
q: the probability of failure (1-p).

Uniform Distribution

All outcomes have the same probability of success. Rolling a dice, 1 to 6.

Poisson Distribution

It is a distribution related to the frequency at which the outcome of an event occurs in a given time interval.

Po(λ), λ is the excepted events in the specified time interval. It is the known average of the events happening in that time interval. X is the number of times the event happened in the specified time…