CAIE A-Level Further Math A2 4.1.3 Pdf and Cdf Questions

Practise deriving probability density and cumulative distribution functions, medians, percentiles and interquartile ranges with Further Mathematics Paper 2 questions and mark…

Exam points

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

[Maximum number: 2]

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 the median value of X.

Median satisfies $\frac{1}{2} \times m \times \frac{6}{5} m=\frac{1}{2}$

OR equivalent use of integration

1
$m=\sqrt{\frac{5}{6}}$

1
Correct value;
accept 0.913

2

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CAIE A-Level Further Math A2 4.1.3 Pdf and Cdf Questions question 1