Find the first two moments for the set of numbers 2,4,6,8
Answers
Step-by-step explanation:
For the first moment, we set s = 1. The formula for the first moment is thus:
(x1x2 + x3 + ... + xn)/n
This is identical to the formula for the sample mean.
The first moment of the values 1, 3, 6, 10 is (1 + 3 + 6 + 10) / 4 = 20/4 = 5.
Second Moment
For the second moment we set s = 2. The formula for the second moment is:
(x12 + x22 + x32 + ... + xn2)/n
The second moment of the values 1, 3, 6, 10 is (12 + 32 + 62 + 102) / 4 = (1 + 9 + 36 + 100)/4 = 146/4 = 36.5.
Third Moment
For the third moment we set s = 3. The formula for the third moment is:
(x13 + x23 + x33 + ... + xn3)/n
The third moment of the values 1, 3, 6, 10 is (13 + 33 + 63 + 103) / 4 = (1 + 27 + 216 + 1000)/4 = 1244/4 = 311.
Higher moments can be calculated in a similar way. Just replace s in the above formula with the number denoting the desired moment.