Distribution

Study of Distribution

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Binomial distribution

The RV $X$ follows the binomial distribution with parameter $n\in \mathbb{N}$ and $p \in [0,1]$

\[X \sim B(n, p)\]

The probability of getting exactly $k$ successes in $n$ independent Bernoulli trails is given by the probability mass function.

\[f(k,n,p) = Pr(k;n,p) = Pr(X=k) = \begin{pmatrix} n \\ k \end{pmatrix} p^k (1-p)^{n-k}\]

• Mean: $\mathbb{E}[X] = np$
• Variance : $\operatorname{Var}(X) = npq = np(1-p)$

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