Financial Risk Manager Part 1
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A sample amount of profit for a certain company for the first 15 weeks of the year is given below:
| Weeks | Amount of the Profit($) |
|---|---|
| 1 | 0 |
| 2 | 7,000 |
| 3 | 13,000 |
| 4 | 13,000 |
| 5 | 20,000 |
| 6 | 23,000 |
| 7 | 25,000 |
| 8 | 27,000 |
| 9 | 34,000 |
| 10 | 41,000 |
| 11 | 60,000 |
| 12 | 66,000 |
| 13 | 76,000 |
| 14 | 77,000 |
| 15 | 96,000 |
What is the difference between the biased and an unbiased estimator of the sample mean?
Exam-Like
Community
TTanishq
A
0
B
1.0
C
3.2
D
4.6
Explanation:
Explanation
The sample mean is always an unbiased estimator of the population mean. This is a fundamental statistical principle:
- Unbiased estimator: An estimator whose expected value equals the true population parameter
- Sample mean (x̄): E(x̄) = μ (population mean)
- Biased estimator: An estimator whose expected value differs from the true population parameter
For the sample mean, there is no difference between the biased and unbiased versions because the sample mean itself is inherently unbiased. The difference between biased and unbiased estimators typically applies to variance estimation, where:
- Sample variance with denominator (n-1) is unbiased
- Sample variance with denominator (n) is biased
However, for the mean, both formulas give the same result, and both are unbiased estimators of the population mean.
Therefore, the difference between the biased and unbiased estimator of the sample mean is 0.
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