I finally figured out how to simulate it and came up with the same answer both ways, sorry to bug everyone. If this is a commonsense statistical answer can someone verify this. Thank you.
I need to know if two things are equivalent:
1) I have a oil/gas prospect that has a probability of success of 70% (make a flowing well) that I have modeled with a lognormal distribution of the potential NPVs. I also have 30% chances of dry hole (assume some negative NPV value). Expected value = 70% of the swansons mean of the +NPV distribution added to 30% of the -NPV.
2) Take my same NPV distribution and sample it 70 times and the other 30 times put the -NPV value. Expected Value=swansons mean
Are these two equivalent?
Summary: When you have a Probability of Success (70%) for a certain lognormal distribution can you just take the constant times your distribution or do you have to sample the 30% of 0's you will get or are they the same?