Notes/UNB/Year 4/Semester 2/STAT2593/2024-01-29.md

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)

# Examples
Examples in posted pdf