The discrete uniform distributionEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

What is a discrete uniform distribution on \{1,\ldots,n\}?
P(X=x) for a discrete uniform distribution on \{1,\ldots,n\}?
E(X) for the discrete uniform distribution on \{1,\ldots,n\}?
Var(X) for the discrete uniform distribution on \{1,\ldots,n\}?
Mean of a fair six-sided die?
Variance of a fair six-sided die?
P(X\le k) for the uniform distribution on \{1,\ldots,n\}?
P(a\le X\le b) for the uniform distribution on \{1,\ldots,n\}?
If E(X)=\mu, what is n?
If Var(X)=\sigma^2, what is n?
What is E(X^2) for the uniform distribution on \{1,\ldots,n\}?
Mean and variance for equally likely values 0,1,\ldots,9?
When is the uniform model appropriate?

Exam questions on The discrete uniform distribution

A fair eight-sided spinner has faces numbered 1 to 8. The random variable $X$ is the number on the face it lands on.
Find $\mathrm{Var}(X)$ .2 marks
The discrete random variable $Y$ takes each of the values $1, 2, \ldots, n$ with equal probability, and $\mathrm{E}(Y)=7.5$ .
Find $\mathrm{Var}(Y)$ .2 marks
A fair ten-sided spinner has faces numbered 0 to 9. The random variable $X$ is the number on the face it lands on.
Find $\mathrm{E}(X)$ and $\mathrm{Var}(X)$ .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).