Definitions [2]
Definition: Bernoulli Trial
In a random experiment, if there are only two outcomes, success and failure, and the sum of the probabilities of these two outcomes is one, then any trial of such an experiment is known as a Bernoulli trial.
Definition: Binomial Distribution
The probability distribution of the number of successes in an experiment consisting of n-Bernoulli trials obtained by the binomial expansion of (q + p )ⁿ is called the binomial distribution.
where p = probability of success and
q = probability of failure
\[P\left(X=r\right)=^{n}C_{r}p^{r}q^{n-r}\] is called probability function.
Formulae [3]
Formula: Mean
\[\mathrm{Mean~(\mu)=E(X)=np}\]
Formula: Variance
\[Variance(\sigma^2)=npq\]
Formula: Standard Deviation
\[\text{Standard deviation }(\sigma)=\sqrt{\mathrm{npq}}\]
