| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2025 |
| Session | April |
| Marks | 6 |
| Topic | Geometric Distribution |
| Type | Determine p from given mean or variance |
| Difficulty | Standard +0.8 This question requires recalling the variance formula for a geometric distribution, solving a quadratic equation to find the parameter p, then computing a cumulative probability. It involves multiple steps with algebraic manipulation and understanding of geometric distribution properties, making it moderately harder than a standard A-level question but not requiring novel insight. |
| 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 |
The discrete random variable $X$ has a geometric distribution. It is given that $\text{Var}(X) = 20$.
Determine $P(X \geq 7)$. [6]
\hfill \mbox{\textit{SPS SPS FM Statistics 2025 Q4 [6]}}