| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | One unknown from sum constraint only |
| Difficulty | Easy -1.3 This is a straightforward S1 question requiring only basic probability axioms (probabilities sum to 1) and standard formula application for expectation and variance. Part (i) involves simple fraction arithmetic, and part (ii) is routine calculation with no conceptual challenges—well below average A-level difficulty. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(x\) | - 2 | - 1 | 0 | 1 | 2 |
| \(\mathrm { P } ( X = x )\) | \(\frac { 1 } { 4 }\) | \(\frac { 1 } { 5 }\) | \(k\) | \(\frac { 2 } { 5 }\) | \(\frac { 1 } { 10 }\) |
4 The table below shows the probability distribution of the random variable $X$.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & - 2 & - 1 & 0 & 1 & 2 \\
\hline
$\mathrm { P } ( X = x )$ & $\frac { 1 } { 4 }$ & $\frac { 1 } { 5 }$ & $k$ & $\frac { 2 } { 5 }$ & $\frac { 1 } { 10 }$ \\
\hline
\end{tabular}
\end{center}
(i) Find the value of the constant $k$.\\
(ii) Calculate the values of $\mathrm { E } ( X )$ and $\operatorname { Var } ( X )$.
\hfill \mbox{\textit{OCR S1 2005 Q4 [7]}}