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Bias Coin: Generate 2 Integers with a biased probability
Now suppose you want to make Monte Carlo Simulation of unfair coin. You determine specific probability Formula Random number
How does the formula work?
If the value of In general, if we would like to get the value of
The expected mean is
How to use the worksheet?Worksheet companion of this biased coins tutorial can be downloaded here. The sample worksheet uses the two methods above to compute unfair coins. Of course, in many cases you may need to use this more general formula to make 2 integers (not only zero and one, but any numbers Every time you press F9, it generates one sampling experiment of Monte Carlo Simulation. If you delete the word “STOP”, every time you press F9, you are not only making one sample of numerical simulation; you will add the statistics of the sampling to all samples results. In this way, actually obtain full simple program of Monte Carlo Simulation. To use the worksheet fully, delete the word “STOP” and press F9 repeatedly. If you don't delete the STOP, the simulation will still work but the result of all experiments are simply copies of the current experiment. Write any letter or number on that Blue cell to reset the counter. The formula for mean and variance are recursive. You may see more explanation about this recursive formula in my tutorial on Recursive Statistics. If you are still confuse on how to use iteration in MS Excel, please read my tutorial on MS Excel Iteration.
Give your comments, questions or suggestions for this tutorial
Preferable reference for this tutorial is Teknomo, Kardi. Monte Carlo Simulation Tutorial. http:\\people.revoledu.com\kardi\ tutorial\Simulation\ |
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to get one of the faces of the coin. If the probability to get zero is 
and the probability to get one is 
, we can generate a biased coin using the following formula 
that unformly distributed is generated according to 
maps the value of 
from 
into range of 
. The 
function will round down all values below 1 into 0 and round down all values between 1 and 
into 1. 
is either -1 or 1, then the formula change into 
. 
is either 
or 
, where 
with some biased probability 
to get 
, then 
and the expected variance is 
or 
and 
)