| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Single-piece PDF with k |
| Difficulty | Moderate -0.3 This is a straightforward S3 question requiring standard techniques: using the pdf integration property (∫f(x)dx = 1) to find 'a', then computing E(X) by integration. Both parts involve routine calculus with no conceptual challenges, making it slightly easier than average but still requiring proper execution of multiple steps. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration |
1 The continuous random variable $X$ has probability density function given by
$$\mathrm { f } ( x ) = \begin{cases} \frac { 2 } { 5 } & - a \leqslant x < 0 \\ \frac { 2 } { 5 } \mathrm { e } ^ { - 2 x } & x \geqslant 0 \end{cases}$$
Find\\
(i) the value of the constant $a$,\\
(ii) $\mathrm { E } ( X )$.
\hfill \mbox{\textit{OCR S3 2010 Q1 [8]}}