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CAIE A-Level Mathematics A2 6.3.1 Continuous Random Variables Questions

Practise working with probability density functions, parameters and probabilities for continuous variables.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • verify and use probability density functions
  • determine unknown constants from density conditions
  • calculate continuous probabilities, means and medians from a density

CAIE A-Level Mathematics A2 6.3.1 Continuous Random Variables Questions question 1

[Maximum number: 3]

A random variable X has probability density function f given by

f(x)={ax−x30⩽x⩽20 otherwise f(x)= \begin{cases}a x-x^{3} & 0 \leqslant x \leqslant \sqrt{2} \\ 0 & \text { otherwise }\end{cases}

where a is a constant.

Show that a=2.

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