2024-01-29 09:56:47 -04:00
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Lecture Topic: Binomial Distribution
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# Requirements of Binomial Experiments
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- (n) independent trials
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- Possible outcomes: success (S) and failure (F)
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- Success probability (p)
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## Formula
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The pmf of binomial rv $X$ depends on two parameters $n$ and $p$. We denote the pmf by $b(x; n,p)$
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$$b(x;n,p) = \{
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\begin{pmatrix}
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n \\
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p \\
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\end{pmatrix}
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p^x(1-p)^{n-x}
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\}$$
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$x = 0, 1, 2, ..., n$
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If X ~ b(x; n,p), then
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1. E(X) = np
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2. V(X) = np(1-p)
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2024-01-29 10:27:36 -04:00
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# Examples
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Examples in posted pdf
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