The first four moments about working mean 28.5 of a distribution are 0.294, 7.144, 42.409 and 454.98. Calculate the moments about the mean. Also evaluate 12,and comment upon the skewness and kurtosis of the distribution.
Answers
Step-by-step explanation:
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Given,
μ1' = 0.294
μ2' = 7.144
μ3'= 42.409
μ4 = 454.98
Mean = 28.5
To find,
We have to find the moments about mean, Skewness, and kurtosis.
Solution,
The moments are 7.057, 152583.24, and 7408.78, and the skewness is 149.07.
We can simply find the moments about mean using the relation:
μ2 = μ2' - μ1'^2
μ2 = 7.144 - (0.294)^2
μ2 = 7.057
μ3 = μ3' - 3μ2'μ1'^2 + 2μ1'^3
μ3 = 42.409 - 3*0.294*7.144 + 2 *76273.57
μ3 = 42.40-6.30 + 152547.14
μ3 = 152583.24
μ4 = μ4' -4μ1'μ3' +6μ2'μ1'^2 -3μ1'^4
μ4 = 454.98 - 49.87 + 3.70 - 0.022
μ4 = 7408.78
Skewness = μ4/μ2^2
= 7408.78/49.70
= 149.07
Hence, the moments are 7.057, 152583.24, and 7408.78, and the skewness is 149.07.