Explanation
To solve this problem, we need to relate the moments about a given point A (raw moments) to the mean and variance (central moments) of the distribution.
1. Identify the given values: Let the point about which moments are taken be A=2. The moments about A=2 are denoted as μ1′,μ2′,μ3′:
2. Calculate the Mean (xˉ): The relationship between the mean and the first raw moment μ1′ about point A is:
Substituting the values:
3. Calculate the Variance (σ2 or μ2): The variance is the second central moment (μ2). The relationship between central moments and raw moments is:
Substituting the given values:
4. Final Answer Pair: The mean of the distribution is 3 and the variance is 15. This corresponds to the coordinate pair (3,15).
Conclusion: By applying the standard formulas for shifting moments, we find that the mean is 3 and the variance is 15.
Correct Option: C) (3,15)
