| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | One unknown from sum constraint only |
| Difficulty | Easy -1.2 This is a straightforward S1 question testing basic probability distribution properties. Part (a) uses the simple constraint that probabilities sum to 1 (0.4 + p + 0.05 + 0.15 + p = 1). Parts (b)-(d) are routine calculations of expectation, cumulative probability, and probability of an inequality. Part (e) applies the standard variance property Var(aX+b) = a²Var(X). All parts require only direct application of formulas with no problem-solving or insight needed. |
| Spec | 2.04a Discrete probability distributions5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| \(x\) | - 4 | - 2 | 1 | 3 | 5 |
| \(\mathrm { P } ( X = x )\) | 0.4 | \(p\) | 0.05 | 0.15 | \(p\) |
\begin{enumerate}
\item The discrete random variable $X$ has probability distribution
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & - 4 & - 2 & 1 & 3 & 5 \\
\hline
$\mathrm { P } ( X = x )$ & 0.4 & $p$ & 0.05 & 0.15 & $p$ \\
\hline
\end{tabular}
\end{center}
(a) Show that $p = 0.2$
Find\\
(b) $\mathrm { E } ( X )$\\
(c) $\mathrm { F } ( 0 )$\\
(d) $\mathrm { P } ( 3 X + 2 > 5 )$
Given that $\operatorname { Var } ( X ) = 13.35$\\
(e) find the possible values of $a$ such that $\operatorname { Var } ( a X + 3 ) = 53.4$\\
\hfill \mbox{\textit{Edexcel S1 2014 Q1 [9]}}