Discrete uniform distributionAQA A-Level Further Maths: Mind map

Exam questions on Discrete uniform distribution

1. A fair eight-sided die, numbered $1$ to $8$, is rolled once. The score $X$ is the number on the face it lands on, and $X$ is modelled by the discrete uniform distribution on $\{1,2,\ldots,8\}$.
   Find the variance of $X$.2 marks
2. The discrete random variable $X$ has a discrete uniform distribution on $\{1,2,\ldots,n\}$, where $n$ is a positive integer. It is given that $E(X)=10.5$.
   Find $P(X>E(X))$.2 marks
3. The discrete random variable $X$ has a discrete uniform distribution on $\{1,2,\ldots,n\}$, so that $P(X=x)=\frac1n$ for $x=1,2,\ldots,n$.
   Prove that $E(X)=\frac{n+1}{2}$.3 marks