| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate E(X) from given distribution |
| Difficulty | Easy -1.8 This is a straightforward application of standard formulas E(X) = Σxp(x) and Var(X) = E(X²) - [E(X)]² with simple arithmetic on given probabilities. It requires only direct recall and calculation with no problem-solving or conceptual challenge—typical of the most routine S1 questions. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| x | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( \mathrm { X } = \mathrm { x } )\) | 0.1 | 0.2 | 0.3 | 0.4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((0\times0.1) + 1\times0.2 + 2\times0.3 + 3\times0.4\) | M1 | \(\geq 2\) non-zero terms correct e.g. \(\div 4\): M0 |
| \(= 2(.0)\) | A1 | |
| \((0^2\times0.1) + 1\times0.2 + 2^2\times0.3 + 3^2\times0.4\ (=5)\) | M1 | \(\geq 2\) non-zero terms correct \(\div 4\): M0 |
| \(-2^2\) | M1 | Indep, ft their \(\mu\). Dep +ve result |
| \(= 1\) | A1 | |
| Total | 5 | \((-2)^2\times0.1+(-1)^2\times0.2+0^2\times0.3+1^2\times0.4\): M2; \(\geq 2\) non-0 correct: M1 \(\div 4\): M0 |
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(0\times0.1) + 1\times0.2 + 2\times0.3 + 3\times0.4$ | M1 | $\geq 2$ non-zero terms correct e.g. $\div 4$: M0 |
| $= 2(.0)$ | A1 | |
| $(0^2\times0.1) + 1\times0.2 + 2^2\times0.3 + 3^2\times0.4\ (=5)$ | M1 | $\geq 2$ non-zero terms correct $\div 4$: M0 |
| $-2^2$ | M1 | Indep, ft their $\mu$. Dep +ve result |
| $= 1$ | A1 | |
| **Total** | **5** | $(-2)^2\times0.1+(-1)^2\times0.2+0^2\times0.3+1^2\times0.4$: M2; $\geq 2$ non-0 correct: M1 $\div 4$: M0 |
---1 The table shows the probability distribution for a random variable X.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
x & 0 & 1 & 2 & 3 \\
\hline
$\mathrm { P } ( \mathrm { X } = \mathrm { x } )$ & 0.1 & 0.2 & 0.3 & 0.4 \\
\hline
\end{tabular}
\end{center}
Calculate $\mathrm { E } ( \mathrm { X } )$ and $\operatorname { Var } ( \mathrm { X } )$.
\hfill \mbox{\textit{OCR S1 2007 Q1 [5]}}