Discrete Binomial Distribution

A kind of Discrete Distribution where $n$ independent and identically distributed Bernoulli Trials are performed, counting the total number of “successes” after n trials each with Probability $p$.

$$X\sim \text{Binomial}(n,p)$$

• $f(x)=\left(\genfrac{}{}{0ex}{}{n}{x}\right)p^x{q}^{n-x}\text{for }x\in \{\mathrm{0..}n\}$
• $E(X)=np$
• $\text{Var}(X)=npq$
• $X_{\text{Bin}}={\sum }_{i=1}^n{X}_i\sim \text{Ber(p)}$