| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | November |
| Marks | 7 |
| Topic | Discrete Probability Distributions |
| Type | Sum or difference of two spinners/dice |
| Difficulty | Moderate -0.3 This is a straightforward probability distribution question requiring systematic enumeration of outcomes from two dice (36 equally likely cases), calculation of expected value and variance using standard formulas. While it requires careful counting and arithmetic across multiple steps (7 marks total), it involves only routine application of AS-level statistics concepts with no conceptual challenges or novel problem-solving. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(x\) | 0 | 1 | 2 | 3 | 4 | 5 |
| P(\(X = x\)) |
The random variable $X$ is defined as the difference (always positive or zero) between the scores when 2 ordinary dice are rolled.
\begin{enumerate}[label=(\roman*)]
\item Copy and complete the probability distribution table for $X$. [2]
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
P($X = x$) & & & & & & \\
\hline
\end{tabular}
\item Find the expectation and variance of $X$. [5]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q2 [7]}}