the four wealthiest people in a particular country are 46,33,27,15 assume that samples of size n=2 are randomly selected with replacement from this population of 4 values?
To find the possible samples of size 2 that can be selected with replacement from the given population, we need to consider all the possible combinations.
Since we have 4 individuals with their corresponding wealth values, let's label them as follows:
- Person A: 46
- Person B: 33
- Person C: 27
- Person D: 15
To find the possible samples of size 2 with replacement, we can select two individuals from this group, considering that we can select the same individual more than once.
There are two main ways to determine the samples:
1. Using a combinatorial approach:
- Sample 1: (Person A, Person A)
- Sample 2: (Person A, Person B)
- Sample 3: (Person A, Person C)
- Sample 4: (Person A, Person D)
- Sample 5: (Person B, Person A)
- Sample 6: (Person B, Person B)
- Sample 7: (Person B, Person C)
- Sample 8: (Person B, Person D)
- Sample 9: (Person C, Person A)
- Sample 10: (Person C, Person B)
- Sample 11: (Person C, Person C)
- Sample 12: (Person C, Person D)
- Sample 13: (Person D, Person A)
- Sample 14: (Person D, Person B)
- Sample 15: (Person D, Person C)
- Sample 16: (Person D, Person D)
2. Using a systematic approach by listing all the possible samples:
- (Person A, Person A)
- (Person A, Person B)
- (Person A, Person C)
- (Person A, Person D)
- (Person B, Person A)
- (Person B, Person B)
- (Person B, Person C)
- (Person B, Person D)
- (Person C, Person A)
- (Person C, Person B)
- (Person C, Person C)
- (Person C, Person D)
- (Person D, Person A)
- (Person D, Person B)
- (Person D, Person C)
- (Person D, Person D)
Please note that since replacement is allowed, the sample (Person A, Person A) is included. It means that Person A can be selected twice, resulting in samples where both values are the same.
So, there are a total of 16 possible samples of size 2 that can be randomly selected with replacement from this population.