| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 8 |
| Topic | Discrete Probability Distributions |
| Type | Multiple unknowns from expectation and variance |
| Difficulty | Standard +0.3 This is a straightforward probability distribution question requiring students to find x using the sum of probabilities equals 1, then calculate E(W) and E(W²) to find variance using the standard formula. Part (b) tests basic knowledge of variance properties. While it involves solving a quadratic and multiple calculation steps (7 marks), the techniques are all standard FS1 content with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| \(w\) | 1 | 2 | 3 | 4 |
| \(P(W = w)\) | 0.25 | 0.36 | \(x\) | \(x^2\) |
The probability distribution for the discrete random variable $W$ is given in the table.
\begin{tabular}{|c|c|c|c|c|}
\hline
$w$ & 1 & 2 & 3 & 4 \\
\hline
$P(W = w)$ & 0.25 & 0.36 & $x$ & $x^2$ \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Show that $\text{Var}(W) = 0.8571$. [7]
\item Find $\text{Var}(3W + 6)$. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR FS1 AS 2021 Q2 [8]}}