Question
Download Solution PDFThe fourth central moment of a mesokurtic distribution is 243. Its standard deviation is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF- If the fourth central moment of a mesokurtic distribution is 243 and the standard deviation is 3, we can calculate the variance and confirm if it aligns with a mesokurtic distribution.
- The fourth central moment (μ₄) is related to the variance (σ²) as follows: μ₄ = σ⁴(κ + 3) - 3σ⁴
- For a mesokurtic distribution, the kurtosis (κ) is 3. Substituting the given values into the equation, we have: 243 = 3⁴(3 + 3) - 3(3⁴) 243 = 81(6) - 3(81) 243 = 486 - 243 243 = 243
- Since the equation holds true, we can conclude that the variance is indeed 243. Taking the square root of the variance, we find: σ = √243 σ = 3
Hence, the standard deviation is 3.
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