How do I draw samples of size 3 with replacement from the population 3, 6, 9, 12.
I know that it there are going to be 4^3=64 samples but I want to know how do i make these samples?

Question

How do I draw samples of size 3 with replacement from the population 3, 6, 9, 12. 
I know that it there are going to be 4^3=64 samples but I want to know how do i make these samples?

anonymous · Answer

|dw:1379096634257:dw|

anonymous · Answer

The fundamental counting principle here is:

Suppose one task can be done in $m$ ways 
Suppose another task can be done in $n$ ways

Then the number of ways to do these two tasks sequentially is $m\times n$

ybarrap · Answer

R has a "sample" function that is useful for this purpose: http://www.r-project.org/ http://stat.ethz.ch/R-manual/R-devel/library/base/html/sample.html

anonymous · Answer

Doing the same task $m$ sequentially $3$ times is give be:$$
m^3
$$

anonymous · Answer

correction
1       2        3       in place of   1   2     1

amistre64 · Answer

it might be good to rename the elements as 0,1,2,3

0000
0001
0002
0003
0010
0011
0012
0013
0020
0021
etc ...

that would be the easiest what to account for them.

amistre64 · Answer

samples of size 3,  even i got confused with all the numbers in the problem ...

amistre64 · Answer

but the concept should still be valid, all i did was draw a set of 4 instead of 3