| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | Mean/expectation of geometric distribution |
| Difficulty | Moderate -0.8 This is a straightforward application of standard geometric distribution formulas requiring only direct substitution into well-known results: P(T=r) = (1-p)^(r-1)p, P(T>r) = (1-p)^r, and E(T) = 1/p. No problem-solving or conceptual insight needed, just routine recall and calculation with p=1/5. |
| Spec | 5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
2 A random variable $T$ has the distribution $\operatorname { Geo } \left( \frac { 1 } { 5 } \right)$. Find\\
(i) $\mathrm { P } ( T = 4 )$,\\
(ii) $\mathrm { P } ( T > 4 )$,\\
(iii) $\mathrm { E } ( T )$.
\hfill \mbox{\textit{OCR S1 2008 Q2 [5]}}