The continuous uniform distributionEdexcel A-Level Further Maths: Flashcards

What these 12 flashcards ask

State the probability density function of X\sim U[a,b].
State E(X) for X\sim U[a,b].
State Var(X) for X\sim U[a,b].
State the cumulative distribution function of U[a,b].
How is P(c<X<d) found for X\sim U[a,b]?
What is the median of a continuous uniform distribution?
Why is the uniform distribution also called rectangular?
What is P(X=c) for a continuous uniform variable?
Write the integral that gives E(X) for U[a,b].
Give the pth percentile of U[a,b].
What error distribution models rounding to the nearest 0.1?
If Var(X)=12 for U[a,b], what is b-a?

Exam questions on The continuous uniform distribution

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
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
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

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).