Would greatly appreciate any help on the math concept here. I’m working in MS Excel, so if anyone can speak to that specifically, that would be an added bonus.
I have a Monte Carlo simulation to illustrate the likelihood of an event happening (let’s say winning on a slot machine). I can make a histogram to show all the different frequencies of the event and their relative likelihoods.
Now, each time the event occurs, it pays some amount of money, which is also variable. I have a second Monte Carlo simulation showing all the different possible payouts and their relative frequencies.
Mathematically, how do I combine these two distributions into a single illustration of what a person might win on the slot machine?
Say I run 1,000 simulations of frequency in Column A ( =NORMINV(RAND(),mean,standard_dev) )
And 1,000 simulations of the winnings in Column B. I had figured I would just make a Column C which is frequency times winnings (Column A times Column B), and plot those 1,000 products on a histogram to show the overall expectation of winning in terms of dollars. But I’m afraid that perhaps it shouldn’t be that simple….
Mathematically, is there a flaw in this logic?