Member-only story
The binomial distribution is one of the most popular distributions in statistics. In order to understand the binomial distribution, it is first necessary to understand binomial experiments.
The binomial experiment
A binomial experiment has the following properties:-
- The experiment consists of n repeated trials.
- Each trial has only two possible outcomes.
- The probability of success, p, is the same for each trial.
- Each trial is independent.
Perhaps the most common example of the binomial experiment where a coin is tossed ten times because:-
- The experiment consists of ten repeated trials.
- Each trial has only two possible outcomes, being heads or tails.
- The probability of success is the same for each trial, being 0.5 in this instance.
- Each trial is independent because each coin flip does not affect the outcome of any other coin flips.
The binomial distribution
The binomial distribution was invented by Swiss mathematician Jacob Bernoull, in a proof published posthumously in 1713, which determined that the probability of k such outcomes in n repetitions is equal to…
