5
votes
Is it true that finite expectation leads to finite entropy?
This post answers the second question: exhibit a discrete distribution with infinite entropy.
The idea is that high entropy is achieved with uniform distributions. We therefore construct a ...
- 330k
3
votes
Derivation of expectation with subscript
Changing the notation might help clear things up. Lacking context, I am guessing about the intended meaning, but let's see where these lead.
Evidently, "$(x_t,x_{t-1})$" is an ordered pair ...
- 330k
2
votes
Expected Value for Complex-Valued Random Variable
Write $e^{i\theta}$ as $\cos(\theta) + i \sin(\theta):$
\begin{align*}
E(Y)
&=\int_0^{2\pi}\frac{g\,e^{i\theta}}{2\pi}\,d\theta\\
&=\int_0^{2\pi}\frac{g\,(\cos(\theta)+i\sin(\theta))}{2\pi}\,d\...
- 4,195
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