Question 3 - A-Level Maths

Exam Board	Edexcel
Module	S2 (Statistics 2)
Year	2016
Session	June
Topic	Continuous Uniform Random Variables
Type	E(g(X)) and Var(g(X)) by integration

The random variable \(R\) has a continuous uniform distribution over the interval [5,9]
1. Specify fully the probability density function of \(R\).
2. Find \(\mathrm { P } ( 7 < R < 10 )\)
The random variable \(A\) is the area of a circle radius \(R \mathrm {~cm}\).
Find \(\mathrm { E } ( \mathrm { A } )\)