Draw all possible samples of size n=3 with replacement from thepopulation 2, 5, and 9.

To draw all possible samples of size n=3 with replacement from the population 2, 5, and 9, we can follow these steps:

1. Start by listing all the elements in the population: 2, 5, and 9.
2. Since we are sampling with replacement, we can choose any element from the population for each position in the sample.
3. To generate all possible samples, we need to consider all the combinations of elements from the population, allowing for repetition.
4. Begin by selecting the first element for the sample. We can choose from 2, 5, or 9.
5. Once the first element is chosen, move on to the second element. Again, we can choose from 2, 5, or 9.
6. Repeat this process for the third element as well.
7. By considering all possible combinations, we can generate all the samples of size n=3 with replacement from the population 2, 5, and 9.

Here are all the possible samples:

Sample 1: (2, 2, 2) Sample 2: (2, 2, 5) Sample 3: (2, 2, 9) Sample 4: (2, 5, 2) Sample 5: (2, 5, 5) Sample 6: (2, 5, 9) Sample 7: (2, 9, 2) Sample 8: (2, 9, 5) Sample 9: (2, 9, 9) Sample 10: (5, 2, 2) Sample 11: (5, 2, 5) Sample 12: (5, 2, 9) Sample 13: (5, 5, 2) Sample 14: (5, 5, 5) Sample 15: (5, 5, 9) Sample 16: (5, 9, 2) Sample 17: (5, 9, 5) Sample 18: (5, 9, 9) Sample 19: (9, 2, 2) Sample 20: (9, 2, 5) Sample 21: (9, 2, 9) Sample 22: (9, 5, 2) Sample 23: (9, 5, 5) Sample 24: (9, 5, 9) Sample 25: (9, 9, 2) Sample 26: (9, 9, 5) Sample 27: (9, 9, 9)

These are all the possible samples of size n=3 with replacement from the population 2, 5, and 9.