The first four moments of a distribution about mean are 0,3.2,3.6,20. The mean value is 11.
Calculate moment about origin

Solution:
The first four moments of a distribution about mean `(bar x=11)` are

`m_1=0`

`m_2=3.2`

`m_3=3.6`

`m_4=20`

Find Moment about origin using Central moments

First Moment about origin
`v_1=bar x`

`v_1=11`

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Second Moment about origin
`v_2=m_2+v_1^2`

`=3.2+11^2`

`=3.2+121`

`=124.2`

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Third Moment about origin
`v_3=m_3+3m_2v_1+v_1^3`

`=3.6+3*3.2*11+11^3`

`=3.6+105.6+1331`

`=1440.2`

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Fourth Moment about origin
`v_4=m_4+4m_3v_1+6m_2v_1^2+v_1^4`

`=20+4*3.6*11+6*3.2*11^2+11^4`

`=20+158.4+2323.2+14641`

`=17142.6`

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