| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | November |
| Marks | 5 |
| Topic | Geometric Distribution |
| Type | Variance of geometric distribution |
| Difficulty | Easy -1.2 This question tests straightforward recall and application of standard distribution formulas. Part (i) requires direct recall of geometric distribution mean and variance formulas. Part (ii) involves solving two simultaneous equations (np=4, np(1-p)=8/3) using standard binomial distribution properties—routine algebraic manipulation with no conceptual challenge or problem-solving insight required. |
| Spec | 5.02d Binomial: mean np and variance np(1-p)5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
\begin{enumerate}[label=(\roman*)]
\item Given that $X \sim \text{Geo}\left(\frac{1}{6}\right)$, write down the values of E($X$) and Var($X$). [2]
\item $Y \sim \text{B}(n, p)$. Given that E($Y$) = 4 and Var($Y$) = $\frac{8}{3}$, find the values of $n$ and $p$. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q1 [5]}}