| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Two unknowns from sum and expectation |
| Difficulty | Moderate -0.8 This is a straightforward S1 question requiring standard probability distribution properties. Part (a) involves writing down the sum-to-1 and expectation equations (routine recall), parts (b-d) involve algebraic manipulation and applying variance formulas. All steps are mechanical applications of learned formulas with no problem-solving insight required, making it easier than average but not trivial due to the multi-step calculation. |
| Spec | 2.04a Discrete probability distributions5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| \(x\) | 1 | 2 | 3 | 4 | 5 |
| \(\mathrm { P } ( X = x )\) | 0.10 | \(p\) | 0.20 | \(q\) | 0.30 |
2. The random variable $X$ has probability distribution
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & 1 & 2 & 3 & 4 & 5 \\
\hline
$\mathrm { P } ( X = x )$ & 0.10 & $p$ & 0.20 & $q$ & 0.30 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Given that $\mathrm { E } ( X ) = 3.5$, write down two equations involving $p$ and $q$.
Find
\item the value of $p$ and the value of $q$,
\item $\operatorname { Var } ( X )$,
\item $\operatorname { Var } ( 3 - 2 X )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2006 Q2 [12]}}