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MathGroup Archive 2005

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Re: How to simulate random samples from crooked coin toss?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58532] Re: [mg58511] How to simulate random samples from crooked coin toss?
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Wed, 6 Jul 2005 03:11:16 -0400 (EDT)
  • References: <200507050557.BAA29457@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com


On Jul 5, 2005, at 1:57 AM, DAN BIKLE wrote:

> Math People,
>
> I'm new to Mathematica so please bear with me.
>
> I have a simple problem I want to solve and I'm looking
> for some ideas to get started on it.
>
> I want to simulate 100 tosses of a crooked coin where
> probability of Heads is 0.6 and Tails is 0.4.
>
> After I figure the coin out, I want to move on to crooked
> dice and crooked card decks.
>
> So, really what I'm looking for has more to do with developing
> a method to simulate the collection of random samples.
>
> I looked around in Help and found a promising sentence:
>
> "Random[distribution] gives a random number with the specified
> statistical distribution."
>
> Then I found a page here which has some clues:
> http://mathworld.wolfram.com/DiscreteDistribution.html
>
> Unfortunately, I'm weak with math notation so the above
> page makes little sense to me.
>
> So, let me put it to you as simply as I can:
>
> I want to define a function that could be called like this:
>
> numberOfHeads = coinTosser[infoAboutCoin, numberOfTosses, head]
> numberOfTails = coinTosser[infoAboutCoin, numberOfTosses, tail]
>
> Once I figure out how to write the above function,
> I could template off of it to build something like this:
>
> numberOfOnes = diceRoller[infoAboutThisDie, numberOfRolls, aOne]
>
> Do any of you have thoughts on how to approach the
> writing of the above functions?

To simulate a crooked coin use the Bernoulli distribution:

<<Statistics`DiscreteDistributions`
coinTosser[infoAboutCoin_,numberOfTosses_,head]:=Count[RandomArray 
[BernoulliDistribution[infoAboutCoin],{numberOfTosses}],1]
coinTosser[infoAboutCoin_,numberOfTosses_,tail]:=Count[RandomArray 
[BernoulliDistribution[infoAboutCoin],{numberOfTosses}],0]

Regards,

Ssezi


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