Means---Moments, etc. for One-dimensional Distributions

Given a one-dimensional distribution, we can define:

• mean:
• n'th moment: dx
• expectation: which ``follows'' from n'th moment by Taylor expansion of . This can be considered as the mean of the random variable .

• n'th central moment:

• Variance: 2nd central moment

• Standard deviation : where is used much more than .

• Note:

  

  a result which is used continuously.