Is it possible that the expected value $\left \langle D \right \rangle$ of a random variable $D$ diverges for $N\rightarrow \infty $ ?
Where $N$ is the number of examples used to calculate the expected value $\left \langle D \right \rangle$.
2026-04-08 12:48:39.1775652519
Divergent Expected Value
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The expected value of a random variable does not depend on the number of samples. What depends on the number of samples is the sample mean, which is
$$\bar D_N = \frac 1N \sum D_i$$
The law of large numbers tells you that if $D \in L^1$ (that is, $E[D]$ is finite) then the sample mean converges to $E[D]$. So to have the sample mean diverge, you have to look at random variables for which the expected value does not exist (or is infinite)