Question
Download Solution PDFLet the first four central moments of a distribution be μ1 = 0, μ2 = -93, μ3 = 0, μ4 = 2.53. The distribution:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF- Based on the provided information regarding the first four central moments of a distribution:
- μ1 = 0 μ2 = -93 μ3 = 0 μ4 = 2.53
- We can deduce the following characteristics of the distribution:
- Symmetry: The fact that the first central moment (μ1) is zero indicates that the distribution possesses symmetricity. A zero value for μ1 suggests that the distribution is centred around its mean, implying the absence of skewness.
- Kurtosis (Platykurtic): The positive value of the fourth central moment (μ4) at 2.53 implies positive kurtosis. Positive kurtosis suggests that the distribution possesses heavier tails and a more peaked shape than a normal distribution. Specifically, the given value of μ4 indicates a platykurtic distribution, signifying lighter tails and a flatter peak compared to a normal distribution.
Hence, based on the provided information, the distribution can be formally described as symmetric and platykurtic.
Last updated on Jul 17, 2025
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