Rectangular distributionAQA A-Level Further Maths: Mind map

Exam questions on Rectangular distribution

1. 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
2. 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
3. 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