| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2020 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate E(X) from given distribution |
| Difficulty | Moderate -0.8 This is a straightforward S1 question requiring two standard steps: finding k by summing probabilities to 1, then calculating E(X) using the formula Σxp(x). It involves only basic arithmetic with given values and direct application of memorized formulas, making it easier than average with no problem-solving or conceptual challenges. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Table with \(P(X=x)\) having values \(\frac{9}{k}, \frac{6}{k}, \frac{5}{k}, \frac{4}{k}, \frac{1}{k}\) for \(x = -1, 2, 3, 4, 7\) | M1 | At least 3 correct probabilities in terms of \(k\) (may be seen used in expression for \(E(X)\)) |
| \(\sum P(X=x) = 1 \Rightarrow \frac{25}{k} = 1\) | M1 | Attempting to use sum of 5 probs \(= 1\) (ft their probabilities) |
| \(k = 25\) | A1 | For \(k=25\) (stated or used correctly) |
| \(E(X) = \frac{1}{25}[-1\times9 + 2\times6 + 3\times5 + 4\times4 + 7\times1]\) | M1 | Attempt at correct expression with at least 3 products (ft their \(k\)-value or letter) |
| \(= \frac{41}{25}\) | A1 | For \(\frac{41}{25}\) or exact equivalent e.g. \(1.64\) |
# Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Table with $P(X=x)$ having values $\frac{9}{k}, \frac{6}{k}, \frac{5}{k}, \frac{4}{k}, \frac{1}{k}$ for $x = -1, 2, 3, 4, 7$ | M1 | At least 3 correct probabilities in terms of $k$ (may be seen used in expression for $E(X)$) |
| $\sum P(X=x) = 1 \Rightarrow \frac{25}{k} = 1$ | M1 | Attempting to use sum of 5 probs $= 1$ (ft their probabilities) |
| $k = 25$ | A1 | For $k=25$ (stated or used correctly) |
| $E(X) = \frac{1}{25}[-1\times9 + 2\times6 + 3\times5 + 4\times4 + 7\times1]$ | M1 | Attempt at correct expression with at least 3 products (ft their $k$-value or letter) |
| $= \frac{41}{25}$ | A1 | For $\frac{41}{25}$ or exact equivalent e.g. $1.64$ |
Correct answer with no incorrect method marks scores 5/5
---\begin{enumerate}
\item The discrete random variable $X$ takes the values $- 1,2,3,4$ and 7 only.
\end{enumerate}
Given that
$$\mathrm { P } ( X = x ) = \frac { 8 - x } { k } \text { for } x = - 1,2,3,4 \text { and } 7$$
find the value of $\mathrm { E } ( X )$\\
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\hfill \mbox{\textit{Edexcel S1 2020 Q1 [5]}}