Rectangular distributionAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

State the pdf of the rectangular distribution on [a,b].
State the mean of a rectangular distribution on [a,b].
State the variance of a rectangular distribution on [a,b].
State the standard deviation of a rectangular distribution on [a,b].
What condition makes a rectangular model appropriate?
Give a situation modelled as rectangular.
Rectangular on [a,b]: formula for P(c<X<d)?
Why is the pdf height \frac{1}{b-a}?
Which factorisation is used in the proof of the mean?
Which factorisation is used in the proof of the variance?
Rectangular on [0,12]: find P(X9).
Why would a rectangular model fail for commuters who know the timetable?

Exam questions on Rectangular distribution

The time, $X$ minutes, that a customer waits for a lift is modelled by a continuous rectangular distribution on the interval $[2, 10]$ .
Find $\mathrm{P}(3<X<5.5)$ , giving your answer as a fraction.2 marks
A length is measured to the nearest centimetre. The rounding error, $E$ cm, is modelled by a continuous rectangular distribution on the interval $[-0.5, 0.5]$ .
Find the probability that the rounding error is more than $0.4$ cm in size, that is $\mathrm{P}(|E|>0.4)$ .2 marks
The continuous random variable $X$ has a rectangular distribution on the interval $[a, b]$ , where $a<b$ , so that $f(x)=\frac{1}{b-a}$ for $a\le x\le b$ and $f(x)=0$ otherwise.
Prove that $\mathrm{E}(X)=\frac{a+b}{2}$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).