Discrete uniform distributionAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

What is P(X=x) for a discrete uniform distribution on \{1,\ldots,n\}?
E(X) for the uniform distribution on \{1,\ldots,n\}?
Var(X) for the uniform distribution on \{1,\ldots,n\}?
When can the discrete uniform distribution be used as a model?
Give a situation that is NOT uniform.
Give a situation that is uniform.
Sum of the first n integers?
Sum of the first n squares?
What is E(X^2) for the uniform distribution?
Mean and variance of a fair six-sided die?
How do you find n from a given mean?
How do you find a probability for a uniform DRV?

Exam questions on Discrete uniform distribution

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
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
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

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).