The continuous uniform distributionEdexcel International A Level Further Maths: Mind map

Exam questions on The continuous uniform distribution

1. The continuous random variable $X$ is uniformly distributed over the interval $[2,8]$.
   Find $E(X)$ and $\text{Var}(X)$.2 marks
2. The length $L$ cm of a rod cut by a machine is modelled by a continuous uniform distribution over the interval $[49,51]$.
   The machine's target length is 50 cm. Find the probability that a rod is within 0.25 cm of the target.2 marks
3. The continuous random variable $X$ is uniformly distributed over the interval $[a,b]$, where $b>a$.
   Show that the cumulative distribution function is $F(x)=\frac{x-a}{b-a}$ for $a\le x\le b$.3 marks