| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| 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 S1 question requiring only direct application of standard formulas for cumulative distribution, probability calculations, and expectation. All parts involve routine calculations with no problem-solving or conceptual challenges—simpler than the typical A-level question which would require more technique integration. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.03a Continuous random variables: pdf and cdf |
| \(y\) | \({ } ^ { - } 2\) | \({ } ^ { - } 1\) | 0 | 1 | 2 |
| \(\mathrm { P } ( Y = y )\) | 0.1 | 0.15 | 0.2 | 0.3 | 0.25 |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.1 + 0.15 + 0.2 = 0.45\) | A1 | |
| \(0.2 + 0.3 = 0.5\) | M1 A1 | |
| \(\sum yP(y) = (-0.2) + (-0.15) + 0 + 0.3 + 0.5 = 0.45\) | M1 A1 | |
| \(3E(Y) - 1 = 0.35\) | M1 A1 | (7) |
| $0.1 + 0.15 + 0.2 = 0.45$ | A1 | |
| $0.2 + 0.3 = 0.5$ | M1 A1 | |
| $\sum yP(y) = (-0.2) + (-0.15) + 0 + 0.3 + 0.5 = 0.45$ | M1 A1 | |
| $3E(Y) - 1 = 0.35$ | M1 A1 | (7) |\begin{enumerate}
\item The discrete random variable $Y$ has the following probability distribution.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$y$ & ${ } ^ { - } 2$ & ${ } ^ { - } 1$ & 0 & 1 & 2 \\
\hline
$\mathrm { P } ( Y = y )$ & 0.1 & 0.15 & 0.2 & 0.3 & 0.25 \\
\hline
\end{tabular}
\end{center}
Find\\
(a) $\mathrm { F } ( 0.5 )$,\\
(b) $\mathrm { P } \left( { } ^ { - } 1 < Y < 1.9 \right)$,\\
(c) $\mathrm { E } ( Y )$,\\
(d) $\mathrm { E } ( 3 Y - 1 )$.\\
\hfill \mbox{\textit{Edexcel S1 Q1 [7]}}