| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Topic | Uniform Distribution |
| Type | Find parameter from variance or other constraint |
| Difficulty | Standard +0.8 This question requires understanding of expectation and variance properties (linearity of expectation, variance scaling by the square), then setting up and solving a system involving the formulas for discrete uniform distributions. While the formulas themselves are standard, students must recognize the distribution type, correctly apply E(aX) = aE(X) and Var(aX) = a²Var(X), recall or derive the mean and variance of a discrete uniform distribution, and solve simultaneous equations involving n² terms. This combines multiple concepts and requires algebraic manipulation beyond routine application, making it moderately challenging for Further Statistics. |
| Spec | 5.02e Discrete uniform distribution5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
The random variable $X$ is equally likely to take any of the $n$ integer values from $m + 1$ to $m + n$ inclusive. It is given that E$(3X) = 30$ and Var$(3X) = 36$.
Determine the value of $m$ and the value of $n$. [7]
\hfill \mbox{\textit{OCR Further Statistics 2021 Q2 [7]}}