Easy -1.8 This is a conceptual recall question testing the fundamental property that for continuous random variables, P(X = any specific value) = 0. No calculation is required—students simply need to recognize this basic definition. This is significantly easier than typical A-level questions which require actual problem-solving or computation.
1 Let \(X\) be a continuous random variable with probability density function given by
$$f ( x ) = \begin{cases} \frac { 3 } { 4 } x ( 2 - x ) & 0 \leq x \leq 2 \\ 0 & \text { otherwise } \end{cases}$$
Find \(\mathrm { P } ( X = 1 )\)
Circle your answer.
0
\(\frac { 1 } { 2 }\)
\(\frac { 3 } { 4 }\)
\(\frac { 27 } { 32 }\)
1 Let $X$ be a continuous random variable with probability density function given by
$$f ( x ) = \begin{cases} \frac { 3 } { 4 } x ( 2 - x ) & 0 \leq x \leq 2 \\ 0 & \text { otherwise } \end{cases}$$
Find $\mathrm { P } ( X = 1 )$\\
Circle your answer.\\
0\\
$\frac { 1 } { 2 }$\\
$\frac { 3 } { 4 }$\\
$\frac { 27 } { 32 }$
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2018 Q1 [1]}}