Moments
It is easy to see by symmetry that for a random variable X having this distribution, its expected value E(X) = 1/2, and that all odd central moments of X are 0.
The law of total variance can be used to find the variance var(X), as follows. For the above set C1, let Y = 0 if X ∈, and 1 if X ∈ . Then:
From this we get:
A closed-form expression for any even central moment can be found by first obtaining the even cumulants
where B2n is the 2nth Bernoulli number, and then expressing the moments as functions of the cumulants.
Read more about this topic: Cantor Distribution
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