| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Sum or combination of independent binomial values |
| Difficulty | Moderate -0.3 Part (i) involves straightforward binomial probability calculations using the formula or tables, and variance recall. Part (ii) requires recognizing that the sum of two independent B(2,1/4) variables follows B(4,1/4), then calculating P(sum=1), which is a standard application but requires slightly more thought than pure recall. Overall, this is slightly easier than average due to being mostly routine calculations with minimal problem-solving. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
3 (i) A random variable, $X$, has the distribution $\mathrm { B } ( 12,0.85 )$. Find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } ( X > 10 )$,
\item $\mathrm { P } ( X = 10 )$,
\item $\operatorname { Var } ( X )$.\\
(ii) A random variable, $Y$, has the distribution $\mathrm { B } \left( 2 , \frac { 1 } { 4 } \right)$. Two independent values of $Y$ are found. Find the probability that the sum of these two values is 1 .
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2011 Q3 [10]}}