Calculating Moments of Distribution: Finding the Moment About 10

[kidia]

I have a question here I will appreciate for any idea,The mean of distribution is 5.The second and third moments about the mean are 20 and 140 respectively.Find the moment of the distribution about 10.

 

[mathman]

All you need to do is use the binomial theorem and take averages.
For the second moment we have
(x-b)²=(x-a+a-b)²
=(x-a)²+2(x-a)(a-b)+(a-b)²

Now assume a is the mean and b is some other value, and take averages.
We the get:
Second moment around b=second moment around a +(a-b)²
(Note that x average =a).

For the third moment, carry out a similar expansion.