# Expected difference between exponentially distributed values

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)