## Probability

# Bernoulli Trials and Binomial Distribution

- If an experiment is conducted by n-Bernoulli's trials and p is the probability of success and q is the probability of failure, then the binomial distribution is given by (q + p)
^{n}(or) B(n, p) - The general term of Binomial distribution

P(r successes) = P(x = r)

\tt \begin{cases}n_{c_{r}} q^{n-r} p^{r}; & {\tt if} \ p \neq q\\ n_{c_{r}} p^{n}; & {\tt if} \ p = q\end{cases}

### View the Topic in this video From 28:19 To 53:40

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1. The probability of r successes in n independent Bernaulli Trials is denoted by P(X = r) and is given by

P(X = r) = ^{n}C_{r} p^{r} q^{n − r},

where p = probability of success

q = probability of failure

and p + q = 1

2. Mean of binomial distribution = np

3. Variance of binomial distribution = npq

4. Standard deviation of binomial distribution \tt = \sqrt{npq}