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Isaac Shoebottom 2024-01-29 09:56:47 -04:00
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UNB/Year 4/Semester 2/STAT2593/2024-01-29.md Normal file
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Lecture Topic: Binomial Distribution
# Requirements of Binomial Experiments
- (n) independent trials
- Possible outcomes: success (S) and failure (F)
- Success probability (p)
## Formula
The pmf of binomial rv $X$ depends on two parameters $n$ and $p$. We denote the pmf by $b(x; n,p)$
$$b(x;n,p) = \{
\begin{pmatrix}
n \\
p \\
\end{pmatrix}
p^x(1-p)^{n-x}
\}$$
$x = 0, 1, 2, ..., n$
If X ~ b(x; n,p), then
1. E(X) = np
2. V(X) = np(1-p)