202405310921
Status: #idea
Tags: Probability Distributions
State: #nascient

Bernoulli Distribution

The mother of all Probability Distributions, because every other distribution can be turned into that if we want to.
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Properties

Take $n$ $i . i . d$ distributed Bernoulli trials, the moment generating function for the entire set of trials (let's call it $Y$ ) will be given by :

E (e^{t Y}) = M (t) = \sum + {k = 0}^{n} n C k p^{k} q^{n - k} e^{t k}

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Relevant Links

Binomial Distribution