I'm a late learner of science & maths.

These problems origin from Asian examinations.

Do you know any books discussing these kind of problems?

Sample queations

Q1

The mean and variance of a finite population P = where

, are defined as follows:

Samples of size 2, , where , are drawn at random from P. the mean of and is denoted by . These means then form a set

a) Show that

b) Show that the mean of all the elemeants of S is equal to

c) Show that the variance of all the elements of S is equal to .

hence deduce that if , this variance tends to .

solution

a)

b)

c)

variance =

as

we have

variance =

as , variance