| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 8 |
| Topic | Geometric Distribution |
| Type | Geometric with multiple success milestones |
| Difficulty | Moderate -0.8 This is a straightforward application of the geometric distribution with standard bookwork questions. Parts (a)-(d) require direct recall of geometric distribution properties (independence assumption, PMF formula, CDF calculation, and variance formula). Part (e) requires minimal contextual reasoning about why independence might fail over a calendar year. No problem-solving or novel insight needed—purely routine application of a single topic. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
A book reviewer estimates that the probability that he receives a delivery of books to review on any one weekday is $0.1$. The first weekday in September on which he receives a delivery of books to review is the $X$th weekday of September.
\begin{enumerate}[label=(\alph*)]
\item State an assumption needed for $X$ to be well modelled by a geometric distribution. [1]
\item Find $P(X = 11)$. [2]
\item Find $P(X \leq 8)$. [2]
\item Find $\text{Var}(X)$. [2]
\item Give a reason why a geometric distribution might not be an appropriate model for the first weekday in a calendar year on which the reviewer receives a delivery of books to review. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR FS1 AS 2021 Q1 [8]}}