| Exam Board | SPS |
|---|---|
| Module | SPS ASFM Statistics (SPS ASFM Statistics) |
| Year | 2021 |
| Session | May |
| Marks | 9 |
| Topic | Discrete Probability Distributions |
| Type | Two unknowns from sum and expectation |
| Difficulty | Moderate -0.8 This is a straightforward application of standard probability distribution formulas. Part (i) requires finding two unknowns using the probability sum and expectation equations, then computing variance using the standard formula—routine but multi-step. Parts (ii) and (iii) are direct applications of E(aX+b) and Var(aX+b) properties, requiring only recall of formulas. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| Score, \(N\) | 1 | 2 | 3 | 4 | 5 |
| Probability | 0.3 | 0.2 | 0.2 | \(x\) | \(y\) |
A spinner has edges numbered 1, 2, 3, 4 and 5. When the spinner is spun, the number of the edge on which it lands is the score. The probability distribution of the score, $N$, is given in the table.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Score, $N$ & 1 & 2 & 3 & 4 & 5 \\
\hline
Probability & 0.3 & 0.2 & 0.2 & $x$ & $y$ \\
\hline
\end{tabular}
\end{center}
It is known that E$(N) = 2.55$.
\begin{enumerate}[label=(\roman*)]
\item Find Var$(N)$. [7]
\item Find E$(3N + 2)$. [1]
\item Find Var$(3N + 2)$. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM Statistics 2021 Q6 [9]}}