| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Piecewise PDF with k |
| Difficulty | Standard +0.3 This is a standard S2 probability density function question requiring routine integration techniques: normalizing the pdf, finding expectation, deriving the cdf, and calculating a probability. All steps follow textbook procedures with straightforward polynomial integration, making it slightly easier than average for A-level but still requiring careful algebraic manipulation across multiple parts. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration5.03e Find cdf: by integration |
A continuous random variable X has probability density function f(x) where
$$f(x) = \begin{cases}
k(x^3 + 2x + 1), & -1 \leq x \leq 0, \\
0, & otherwise
\end{cases}$$
where k is a positive integer.
\begin{enumerate}[label=(\alph*)]
\item Show that k = 3. [4]
\end{enumerate}
Find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item E(X), [4]
\item the cumulative distribution function F(x), [4]
\item P(−0.3 < X < 0.3). [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q7 [15]}}