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

*To*: mathgroup at smc.vnet.net*Subject*: [mg58529] Re: How to simulate random samples from crooked coin toss?*From*: dh <dh at metrohm.ch>*Date*: Wed, 6 Jul 2005 03:11:14 -0400 (EDT)*References*: <dad7vt$41$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Dan, If you want to simulate the coin tossing problem, remember that Random[ ] gives a uniformly distributed pseudorandom Real in the range 0 to 1. Therefore, if we want to simulate an event with probability P, we check if the outcome of Random is below P or not. E.g. How many heads in n tosses with a crooked coin with P=0.6: Count[ Table[ If[Random[]<P,1,0] ,{n} ] ,1] For y dice, you would check if the outcome of Random =x is: x<1/6, 1/6<=x<2/6,.. depending on how many eyes you want. An additional note: if you only want a function like: > numberOfHeads = coinTosser[infoAboutCoin, numberOfTosses, head] the problem can be solved without simulations For your purpose, to describe a coin (dice, cards) you have to specify the propability that a certain event happens, e.g. "Head", call it Ph. A fine coin would have Ph=0.5, a croocked coin e.g. Ph=0.6. Now as your coin tosses are all independent, the mean number of Heads in n tosses will simply be: n Ph sincerely, Daniel 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? > > -Dan

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

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

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

**Any ideas about solving an underdetermined system?**