We'll start with the binomial distribution for discrete variables in binomial experiments. A binomial experiment has only two possible outcomes: success or failure. It also satisfies the following requirements:
- Each trial is independent of the others.
- The probability of success is always the same.
An example of a binomial experiment is the coin toss experiment.
Now, let's assume that the experiment consists of n trials. x of them are successful, while the probability of success at each trial is p. The formula for a binomial PMF of variable X (not to be confused with x) is as follows:
Here, is the binomial coefficient. ...
