Question 7 - A-Level Maths

Exam Board	Edexcel
Module	S2 (Statistics 2)
Year	2010
Session	January
Topic	Central limit theorem
Type	Deriving sampling distribution

A bag contains a large number of coins. It contains only \(1 p\) and \(2 p\) coins in the ratio \(1 : 3\)
1. Find the mean \(\mu\) and the variance \(\sigma ^ { 2 }\) of the values of this population of coins.
A random sample of size 3 is taken from the bag.
List all the possible samples.
Find the sampling distribution of the mean value of the samples.