| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Two unknowns from sum and expectation |
| Difficulty | Moderate -0.8 This is a standard two-equation, two-unknown problem requiring only routine application of probability axioms (sum = 1) and expectation formula. The arithmetic is straightforward with no conceptual challenges, making it easier than average but not trivial since it requires setting up and solving simultaneous equations. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(x\) | - 3 | - 1 | 0 | 4 |
| \(\mathrm { P } ( X = x )\) | \(a\) | \(b\) | 0.15 | 0.4 |
| Answer | Marks | Guidance |
|---|---|---|
| \(a + b = 0.45\) and \(-3a - b + 1.6 = 0.75\) giving \(a = 0.2\) and \(b = 0.25\) | B1, M1, A1, A1 | Correct sum probs = 1 o.e.; Attempt at \(\Sigma p = 0.75\); Correct \(a\); Correct \(b\) |
$a + b = 0.45$ and $-3a - b + 1.6 = 0.75$ giving $a = 0.2$ and $b = 0.25$ | B1, M1, A1, A1 | Correct sum probs = 1 o.e.; Attempt at $\Sigma p = 0.75$; Correct $a$; Correct $b$ | **Total: [4]**
---1 The probability distribution of the discrete random variable $X$ is shown in the table below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$x$ & - 3 & - 1 & 0 & 4 \\
\hline
$\mathrm { P } ( X = x )$ & $a$ & $b$ & 0.15 & 0.4 \\
\hline
\end{tabular}
\end{center}
Given that $\mathrm { E } ( X ) = 0.75$, find the values of $a$ and $b$.
\hfill \mbox{\textit{CAIE S1 2010 Q1 [4]}}