CAIE A-Level Further Math A2 4.1.1 Piecewise Density Functions Questions

Practise finding constants and probabilities from piecewise probability density functions with Further Mathematics Paper 2 questions and mark schemes.

Exam points

Apply de Moivre's theorem to powers and roots of complex numbers.

[Maximum number: 1]

The continuous random variable X has probability density function f given by

f(x)= \begin{cases}0 & x<0 \\ \frac{6}{5} x & 0 \leqslant x \leqslant 1 \\ \frac{6}{5} x^{-4} & x>1\end{cases}

Find P(X>1).

$\mathrm{P}(X>1)=1-\frac{1}{2} \times 1 \times \frac{6}{5}=\frac{2}{5}$

OR

1

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CAIE A-Level Further Math A2 4.1.1 Piecewise Density Functions Questions question 1