Edexcel A-Level Mathematics A2 S2.2.2 Probability Density and Cumulative Distribution Functions Questions

Practise using probability densities and cumulative distribution functions to calculate interval probabilities with verified Edexcel IAL questions.

Exam points

use probability densities and cumulative distribution functions to calculate probabilities

[Maximum number: 6]

A random variable X has probability density function given by

f(x)=\left\{\begin{array}{cc} \frac{1}{4} & -\frac{1}{2} \leqslant x<\frac{1}{2} \\ 2 x-\frac{3}{4} & \frac{1}{2} \leqslant x \leqslant k \\ 0 & \text { otherwise } \end{array}\right.

where k is a positive constant.

(a)

Sketch the graph of f(x)

[ 2 ]

(b)

By forming and solving an equation in k, show that k=1.25

[ 4 ]

Area $=\frac{1}{4}+\frac{1}{2}\left(\frac{1}{4}+2 k-\frac{3}{4}\right)\left(k-\frac{1}{2}\right)=1$ or $\frac{1}{4}\left(k+\frac{1}{2}\right)+\frac{1}{2}(2 k-1)\left(k-\frac{1}{2}\right)=1$ or
$\frac{1}{4}+\left[\left(k^{2}-\frac{3}{4} k\right)-\left(\frac{1}{2}^{2}-\frac{3}{8}\right)\right]=1$

A1

$k=1.25^{*}$

A1 *

All question bank results loaded

Edexcel A-Level Mathematics A2 S2.2.2 Probability Density and Cumulative Distribution Functions Questions question 1

Question (a)

Question (b)