I'm a late learner of science & maths.
These problems origin from Asian examinations.
Do you know any books discussing these kind of problems?
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 .
as , variance