Properties of binomial distribution

Answer

The Binomial distribution describes a behavior of a random variable x where the following conditions apply;

1. Consists of n indentical and independent trial.
2. There are only two possible outcomes on each trial- success and failure.
3. The probability of success p is the same for each outcome.

Binomial distribution CDF ; $F\left(x;p,n\right)=\sum _{i=0}^x\left(\begin{array}{c}n\\ i\end{array}\right){\left(p\right)}^i{\left(1-p\right)}^{(n-i)}$

Binomial Distribution PMF; $P\left(x;p,n\right)=\left(\begin{array}{c}n\\ x\end{array}\right){\left(p\right)}^z{\left(1-p\right)}^{(n-x)} for x=0,1,2,3.......n$

where $\left(\begin{array}{c}n\\ x\end{array}\right)=\frac{n!}{x! (n-x)!}$

Yes · 0 No · 0 Add Comment · 0

Add ·

Report