Page 77 - Applied Statistics with R

5.3. SIMULATION 77

We’ll look at two very simple examples here, however simulation will be a topic
we revisit several times throughout the course.

5.3.1 Paired Differences

Consider the model:

2
, , … , 1 ∼ ( , )
1
11
12
2
, , … , 2 ∼ ( , )
21
22
2
2
Assume that = 6, = 5, = 4 and = 25.
2
1
Let
1
̄
= ∑ 1
1

=1
1
̄
= ∑ 2
2

=1
̄
̄
= − .
2
1
Suppose we would like to calculate (0 < < 2). First we will need to obtain
the distribution of .
Recall,
2
̄
∼ ( , )
1
1
and
2
̄
∼ ( , ) .
2
2
Then,
2 2 4 4
̄
̄
= − ∼ ( − , + ) = (6 − 5, + ) .
1
1
2
2
25 25
So,
2
∼ ( = 1, = 0.32).