| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Two unknowns from sum and expectation |
| Difficulty | Standard +0.3 This is a standard S1 probability distribution question requiring systematic application of basic principles: probabilities sum to 1, expectation formula, and variance properties. While it has multiple parts (6 marks total), each step follows directly from textbook methods with no novel insight needed. The two-unknown system in part (b) is straightforward algebra. This is slightly easier than average because it's highly structured and procedural, though the multiple parts prevent it from being trivial. |
| Spec | 2.04a Discrete probability distributions5.02b Expectation and variance: discrete random variables5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( X = x )\) | \(3 a\) | \(2 a\) | \(b\) |
6. The discrete random variable $X$ has probability function
$$\mathrm { P } ( X = x ) = \left\{ \begin{array} { c l }
a ( 3 - x ) & x = 0,1,2 \\
b & x = 3
\end{array} \right.$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { P } ( X = 2 )$ and complete the table below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$x$ & 0 & 1 & 2 & 3 \\
\hline
$\mathrm { P } ( X = x )$ & $3 a$ & $2 a$ & & $b$ \\
\hline
\end{tabular}
\end{center}
Given that $\mathrm { E } ( X ) = 1.6$
\item Find the value of $a$ and the value of $b$.
Find
\item $\mathrm { P } ( 0.5 < X < 3 )$,
\item $\mathrm { E } ( 3 X - 2 )$.
\item Show that the $\operatorname { Var } ( X ) = 1.64$
\item Calculate $\operatorname { Var } ( 3 X - 2 )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2009 Q6 [15]}}