| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2020 |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Exponential Distribution |
| Type | Calculate probability with given parameter |
| Difficulty | Standard +0.3 This is a straightforward application of exponential distribution formulas. Part (a) requires direct substitution into P(X > 500) = e^{-λx}, while part (b) needs recognizing that E(X) = 1/λ = 500, then computing P(X ≥ 1500). Both parts are standard textbook exercises with no conceptual challenges beyond knowing the exponential distribution properties, making this slightly easier than average for A-level Further Maths Statistics. |
| Spec | 5.03a Continuous random variables: pdf and cdf |
The lifetimes, in hours, of light bulbs have an exponential distribution with parameter $\frac{1}{500}$. Each bulb is tested and rejected if the lifetime is less than 500 hours.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that a bulb of this type has a lifetime of more than 500 hours. [4]
\item Find the probability that the lifetime is at least three times the expected lifetime. [6]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2020 Q4 [10]}}