Binomial distribution and when to use it.

easy

Answer

$X ~ Binomial(n, p): number of successes in n independent Bernoulli(p) trials.$
$P(X = k)\; = \;C(n, k)\; \cdot \;p^{k}\; \cdot \;(1 - p)$
$\operatorname{Var}(X)\; = \;\mathrm{np}(1 - p)$
$Use it for: A/B testing (successes out of n visitors), quality inspection (defects out of n items), any bounded count of independent trials.$
$When n is large and p is small, approximate by Poisson(np).$

Check yourself — multiple choice

$P(X = k)\; = \;p^{k}$
Sum of n i.i.d. Bernoulli(p); E[X]=np, $\operatorname{Var}(X) = \mathrm{np}(1 - p)$ ; use for A/B tests, quality inspection
Only for continuous
Var = n

Binomial = n iid Bernoulli(p); mean np, variance np(1-p).

#distributions#probability

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