| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate Var(X) from table |
| Difficulty | Easy -1.2 This is a straightforward application of standard variance formula from a given probability distribution table. Part (i) requires simple verification of E(X) using the definition (sum of r×P(X=r)), and part (ii) requires calculating Var(X) = E(X²) - [E(X)]² using the same table. Both are routine textbook exercises with no problem-solving or conceptual challenges beyond direct formula application. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(r\) | 10 | 20 | 30 | 40 |
| \(\mathrm { P } ( X = r )\) | 0.2 | 0.3 | 0.3 | 0.2 |
3 The table shows the probability distribution of the random variable $X$.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$r$ & 10 & 20 & 30 & 40 \\
\hline
$\mathrm { P } ( X = r )$ & 0.2 & 0.3 & 0.3 & 0.2 \\
\hline
\end{tabular}
\end{center}
(i) Explain why $\mathrm { E } ( X ) = 25$.\\
(ii) Calculate $\operatorname { Var } ( X )$.
\hfill \mbox{\textit{OCR MEI S1 Q3 [4]}}