The continuous uniform distributionEdexcel 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 $[2,10]$.
   Given that $\mathrm{P}(X<c)=0.35$, find the value of $c$.2 marks
2. The continuous random variable $Y$ is uniformly distributed over the interval $[a,b]$. The mean of $Y$ is $9$ and the variance of $Y$ is $12$.
   Find $\mathrm{P}(Y>11)$.2 marks
3. The continuous random variable $X$ has a continuous uniform distribution over the interval $[a,b]$, where $a<b$.
   Show by integration that $\mathrm{E}(X)=\frac{a+b}{2}$.3 marks