| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Exponential Distribution |
| Type | Calculate probability with given parameter |
| Difficulty | Moderate -0.8 This is a straightforward application of the negative exponential distribution requiring only direct substitution into standard formulas. Part (i) is pure recall (λ = 1/400), part (ii) is a standard CDF calculation P(T < 500) = 1 - e^(-500/400), and part (iii) uses the median formula solving 0.5 = 1 - e^(-m/400). All three parts are textbook exercises with no problem-solving or novel insight required, making this easier than average for A-level. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03f Relate pdf-cdf: medians and percentiles |
6 The random variable $T$ is the lifetime, in hours, of a randomly chosen battery of a particular type. It is given that $T$ has a negative exponential distribution with mean 400 hours.\\
(i) Write down the probability density function of $T$.\\
(ii) Find the probability that a battery of this type has a lifetime that is less than 500 hours.\\
(iii) Find the median of the distribution.\\
\hfill \mbox{\textit{CAIE FP2 2019 Q6 [6]}}