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A binomial random variable \(X\) following the distribution \(\mathcal{B}(n,p)\) can be modeled as:
The sum of \(n\) independent and identically distributed Bernoulli variables \(B(p)\).
The sample mean of \(n\) independent Bernoulli variables \(B(p)\).
A single Bernoulli trial where the probability of success is \(n\times p\).
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