| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate E(X) from given distribution |
| Difficulty | Easy -1.3 This is a straightforward application of standard formulas for E(X) and Var(X) from a discrete probability distribution, followed by routine use of E(aX) = aE(X) and SD(aX) = a·SD(X). All values are given explicitly in a table requiring only arithmetic calculations with no problem-solving or conceptual insight needed. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| \(r\) | 2 | 3 | 4 | 5 | 6 | 7 |
| \(\mathrm { P } ( X = r )\) | 0.03 | 0.07 | 0.27 | 0.49 | 0.13 | 0.01 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | E(X) = 4.65 |
| Var(X) = 0.8675 | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1a |
| 1.1 | BC |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (b) | (i) |
| [1] | 1.1 | BC allow 3.0225 |
| 1 | (b) | (ii) |
| [1] | 1.1 | BC allow 0.6054 |
Question 1:
1 | (a) | E(X) = 4.65
Var(X) = 0.8675 | B1
B1
[2] | 1.1a
1.1 | BC
BC
1 | (b) | (i) | E(birds leaving nest) = 3.02 | B1
[1] | 1.1 | BC allow 3.0225
1 | (b) | (ii) | Sd(birds leaving nest) = 0.605 | B1
[1] | 1.1 | BC allow 0.60541 The random variable $X$ represents the clutch size (the number of eggs laid) by female birds of a particular species. The probability distribution of $X$ is given in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
$r$ & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
$\mathrm { P } ( X = r )$ & 0.03 & 0.07 & 0.27 & 0.49 & 0.13 & 0.01 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find each of the following.
\begin{itemize}
\item $\mathrm { E } ( X )$
\item $\operatorname { Var } ( X )$
\end{itemize}
On average 65\% of eggs laid result in a young bird successfully leaving the nest.
\item \begin{enumerate}[label=(\roman*)]
\item Find the mean number of young birds that successfully leave the nest.
\item Find the standard deviation of the number of young birds that successfully leave the nest.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2021 Q1 [4]}}