Hey Tuufless.

You might want to consider an indicator function that becomes 1 if an exchange is made and 0 otherwise.

In terms of the number of sales, this is just the sum of these indicator variables.

In terms of the indicator variables if you have a distribution of money for the buyer (call it B) and a distribution of the sellers prices (call it P) then the indicator I will be given by I = 1 if (P-B) >= 0 and 0 if P-B < 0.

So now you need to find a random variable where P-B >= 0 and if you have the joint distribution of P and B, then you can find the region of integration where this is met and create a random variable from this sub-set and find its expectation.