| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate Var(X) from table |
| Difficulty | Easy -1.2 This is a straightforward S1 question requiring only basic application of standard formulas for E(X) and Var(X) with a simple two-value distribution. Part (i) is direct substitution, and part (ii) is a 'show that' proof requiring Var(X) = E(X²) - [E(X)]² with minimal algebraic manipulation. This is easier than average A-level content as it's purely mechanical with no problem-solving or insight required. |
| Spec | 5.02b Expectation and variance: discrete random variables |
| \(x\) | 0 | 2 |
| \(\mathrm { P } ( X = x )\) | \(a\) | \(1 - a\) |
7 The probability distribution of a discrete random variable, $X$, is shown below.
\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
$x$ & 0 & 2 \\
\hline
$\mathrm { P } ( X = x )$ & $a$ & $1 - a$ \\
\hline
\end{tabular}
\end{center}
(i) Find $\mathrm { E } ( X )$ in terms of $a$.\\
(ii) Show that $\operatorname { Var } ( X ) = 4 a ( 1 - a )$.
\hfill \mbox{\textit{OCR S1 2011 Q7 [5]}}