I have a set of values with probabilities that are exponentially distributed with a given $\lambda$ parameter. If I take 32 values at random based on the probability density, how can I compute the total difference between the maximum and each other value? That is, if my values are $v_i$ with $i < 32$ and the maximum is $v_m$, I want to compute the expected value of

$\sum\limits_{i=0}^{32} (v_m - v_i)$

Any ideas on how to compute this? At this point I'm stuck and don't even know how to compute the expected maximum, $v_m$.

As an example, let's say my values and their corresponding probabilities are, with $\lambda=10$:

value (probability):

55 (.33)
70 (.22)
47 (.15)
31 (.10)
21 (.07)
14 (.04)
9 (.03)
6 (.02)
4 (.01)

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