Calculating Moments of Distribution: Finding the Moment About 10

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SUMMARY

The discussion focuses on calculating the moment of a distribution about the value 10, given that the mean is 5, with the second and third moments about the mean being 20 and 140, respectively. Using the binomial theorem, the second moment around a different point can be derived by the formula: second moment around b = second moment around a + (a-b)². A similar approach is suggested for calculating the third moment, emphasizing the importance of taking averages in these calculations.

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kidia
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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.
 
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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.
 

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