Further A-Level Mathematics Year 2 Statistics 1: Geometric and Negative Binomial Distributions
Students learn how to recognise and use the geometric and negative binomial distributions throughout this unit. Later, as learning progresses, they find the mean and variance of both distributions.
Lessons on Geometric and Negative Binomial Distributions
Prerequisite Knowledge
From Statistics 1
From Further Statistics 1 AS
Success Criteria
Teaching Points
P(X=r)=(1-p)^{r-1} p \ \ \ \ \ x = 1, 2, 3, ...
E(x)=\frac{1}{p}
\operatorname{Var}(x)=\frac{1-p}{p^{2}}
p(X=x)=\left(\begin{array}{c}x-1 \\ r-1\end{array}\right) p^{r}(1-p)^{x-r}\ x = r, r + 1, ...
E(x)=\frac{r}{p}
\operatorname{Var}(x)=\frac{r(1-p)}{p^{2}}
Misconceptions
P(X \leq x)=1-(1-p)^{x}
P(X>x)=(1-p)^{x}
P(X \geqslant x)=(1-p)^{x-1}
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