| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Sum or product of two independent values |
| Difficulty | Moderate -0.3 This is a straightforward S1 question testing basic discrete probability distributions. Part (i) requires routine calculation of E(Y) and Var(Y) using standard formulas. Parts (ii) and (iii) involve listing simple cases and multiplying independent probabilities—no complex reasoning or novel insight required. Slightly easier than average due to small sample spaces and direct application of independence. |
| Spec | 5.02b Expectation and variance: discrete random variables |
| \(y\) | 1 | 2 | 3 |
| \(\mathrm { P } ( Y = y )\) | 0.2 | 0.3 | 0.5 |
| \(z\) | 1 | 2 | 3 |
| \(\mathrm { P } ( Z = z )\) | 0.1 | 0.25 | 0.65 |
6 The probability distribution for a random variable $Y$ is shown in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
$y$ & 1 & 2 & 3 \\
\hline
$\mathrm { P } ( Y = y )$ & 0.2 & 0.3 & 0.5 \\
\hline
\end{tabular}
\end{center}
(i) Calculate $\mathrm { E } ( Y )$ and $\operatorname { Var } ( Y )$.
Another random variable, $Z$, is independent of $Y$. The probability distribution for $Z$ is shown in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
$z$ & 1 & 2 & 3 \\
\hline
$\mathrm { P } ( Z = z )$ & 0.1 & 0.25 & 0.65 \\
\hline
\end{tabular}
\end{center}
One value of $Y$ and one value of $Z$ are chosen at random. Find the probability that\\
(ii) $Y + Z = 3$,\\
(iii) $Y \times Z$ is even.
\hfill \mbox{\textit{OCR S1 2008 Q6 [11]}}