Moment of distribution

1. Apr 11, 2006

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.

Last edited: Apr 11, 2006
2. Apr 12, 2006

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.