2024-01-29 09:56:47

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

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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)
+