To compute the possible samples of size \( n=2 \) from the given population of assets (41, 34, 21, 12), we can consider the sampling process with replacement.
Population Values:
- \( A_1 = 41 \)
- \( A_2 = 34 \)
- \( A_3 = 21 \)
- \( A_4 = 12 \)
Since we are sampling with replacement, each sample can include any of the four values for each selection. The size of each sample is \( n=2 \), and there are \( 4 \) choices for the first pick and \( 4 \) choices for the second pick.
Possible Samples
We need to list all combinations taking into account that the sampling is done with replacement:
- \( (41, 41) \)
- \( (41, 34) \)
- \( (41, 21) \)
- \( (41, 12) \)
- \( (34, 41) \)
- \( (34, 34) \)
- \( (34, 21) \)
- \( (34, 12) \)
- \( (21, 41) \)
- \( (21, 34) \)
- \( (21, 21) \)
- \( (21, 12) \)
- \( (12, 41) \)
- \( (12, 34) \)
- \( (12, 21) \)
- \( (12, 12) \)
Summary
The total number of possible samples of size \( n=2 \) from the population of 4 people, when sampled with replacement, is \( 4^2 = 16 \).
These are all the combinations we could form with the given population. Each pair represents a sample drawn from the original population with replacement.