| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Multiple unknowns from expectation and variance |
| Difficulty | Standard +0.3 This is a standard S1 probability distribution question requiring systematic application of expectation and variance formulas. While it has multiple parts and requires solving simultaneous equations from the given condition Var(X) = E(X²), the techniques are routine and well-practiced. The question is slightly easier than average because the condition E(X) = 0 (from Var(X) = E(X²)) immediately simplifies the algebra, and all subsequent parts follow mechanically from standard formulas. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| \(x\) | - 4 | - 3 | 1 | 2 | 5 |
| \(\mathrm { P } ( X = x )\) | \(a\) | \(b\) | \(a\) | \(b\) | 0.2 |
4. The discrete random variable $X$ has probability distribution
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & - 4 & - 3 & 1 & 2 & 5 \\
\hline
$\mathrm { P } ( X = x )$ & $a$ & $b$ & $a$ & $b$ & 0.2 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { E } ( X )$ in terms of $a$ and $b$
For this probability distribution, $\operatorname { Var } ( X ) = \mathrm { E } \left( X ^ { 2 } \right)$
\item \begin{enumerate}[label=(\roman*)]
\item Write down the value of $\mathrm { E } ( X )$
\item Find the value of $a$ and the value of $b$
\end{enumerate}\item Find $\operatorname { Var } ( 1 - 3 X )$
Given that $Y = 1 - X$, find
\item \begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( Y < 0 )$
\item the largest possible value of $k$ such that $\mathrm { P } ( Y < k ) = 0.2$
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2018 Q4 [13]}}