CAIE A-Level Further Math A2 4.1.4 Pdf and Cdf Questions

Practise finding probability density and cumulative distribution functions after transforming continuous random variables with Further Mathematics Paper 2 questions and mark…

Exam points

Find probability density or cumulative distribution functions after transforming a continuous random variable.

[Maximum number: 3]

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

f(x)= \begin{cases}\frac{1}{6}\left(x^{-\frac{1}{3}}-x^{-\frac{2}{3}}\right) & 1 \leqslant x \leqslant 27 \\ 0 & \text { otherwise }\end{cases}

Find the probability density function of Y.

$\mathrm{G}(y)=\frac{1}{4}\left(y^{2}-2 y+1\right)$
Using $y=x^{\frac{1}{3}}$ in their F(x).

$\mathrm{g}(y)=\frac{1}{2}(y-1)$
Correct, AEF, 0 otherwise not required.

For $1 \leqslant y \leqslant 3$
Seen anywhere, correct variable.

3

All question bank results loaded

CAIE A-Level Further Math A2 4.1.4 Pdf and Cdf Questions question 1