The first four moments of a distribution about the value 4 are 1,4,10,45.
Calculate moment about mean

Solution:
The first four moments of a distribution about the value 4 are
`M_1=1`

`M_2=4`

`M_3=10`

`M_4=45`

Find Central moments using Moments about the value 4

First Central Moment
`m_1=0`

---

Second Central Moment
`m_2=M_2-M_1^2`

`=4-1^2`

`=4-1`

`=3`

---

Third Central Moment
`m_3=M_3-3M_2M_1+2M_1^3`

`=10-3*4*1+2*1^3`

`=10-12+2`

`=0`

---

Fourth Central Moment
`m_4=M_4-4M_3M_1+6M_2M_1^2-3M_1^4`

`=45-4*10*1+6*4*1^2-3*1^4`

`=45-40+24-3`

`=26`

---

---