The first four moments of a distribution about x=2 are 1,2.5,5.5 and 1 | Statistics I 2080

Statistics I20805 marksNumerical: Moments, skewness, kurtosisMoments

The first four moments of a distribution about x=2 are 1,2.5,5.5 and 16. Calculate the first four moments about the mean. Test the skewness and kurtosis. Interpret the results. [5]

Moments about $x = 2$ (arbitrary origin $a = 2$ ): $\mu1' = 1, \quad \mu2' = 2.5, \quad \mu3' = 5.5, \quad \mu4' = 16$ --- First: $\mu1 = 0$ Second: $\mu2 = \mu2' - (\mu1')^2 = 2.5 - 1 = 1.5$ Third: $\mu3 = \mu3' - 3\mu2'\mu1' + 2(\mu1')^3 = 5.5 - 3(2.5)(1) + 2(1) = 5.5 - 7.5 + 2 = 0$ Four...

Moments about $x = 2$ (arbitrary origin $a = 2$): $$\mu1' = 1, \quad \mu2' = 2.5, \quad \mu3' = 5.5, \quad \mu4' = 16$$ --- First: $$\mu1 = 0$$ Second: $$\mu2 = \mu2' - (\mu1')^2 = 2.5 - 1 = 1.5$$ Third: $$\mu3 = \mu3' - 3\mu2'\mu1' + 2(\mu1')^3 = 5.5 - 3(2.5)(1) + 2(1) = 5.5 - 7.5 + 2 = 0$$ Four...

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