Prerequisites

Distributions

Binomial Distribution

Imagine you are asked to calculate the probability of getting a heads 50 Times out of a coin that is a tossed 90 Times. In such case to calculate the probability of this event we can formulate a basic formulae and we will try to get a basic all inclusive applicable formulae.

Actual Definition

IF an experiment has two outcomes ( Success & Failure ) is repeated $n$ times such an experiment is categorized as binomial distribution.

Suppose the random variable $X$ Denotes the number of successes in $n$ trials and let $P$ be the probability of success in each trial $X-B(n,p)$

$$P(X=x)=C_r^n{p}^r{q}^{n-r}$$

Note Z

• Mean of the binomial distribution is $n\times p$
• Variance of binomial distribution is $n\times p\times (1-p)$

References

Information

• date: 2025.03.21
• time: 17:33