Re: Setting up a probability problem
- To: mathgroup at smc.vnet.net
- Subject: [mg22195] Re: [mg22150] Setting up a probability problem
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Thu, 17 Feb 2000 01:24:32 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
on 00.2.16 4:35 PM, Ron Lenk at Ron.Lenk at fairchildsemi.com wrote: > > > I'm having trouble figuring out the mathematical formulation of this problem. > I have n events, each of which has probability P (say 20%) of occurring at any > given time. How large does n need to be in order to give me a confidence level > c > (say 90%) that I have m (say 5) events occurring simultaneously? Help in > clarifying my thinking would be appreciated. > > > From your formulation it sounds as if "n events, each of which has probability P (say 20%) of occurring at any given time" is the same as having n trials of a single event with probability 0.2 of occuring (and 0.8 of not occurring). If so then what you have is just the binomial distribution BinomialDistribution[n,1/5] (from the Statistics`DiscreteDistributions` package). (I am also assuming that you mean a confidence level of 90% that you get at least 5 events occuring.) So now you want to find the value of n such that 1 -CDF[BinomialDistribution[n, 0.2], 4] >= 0.90. This can be done with : In[26]:= FixedPoint[If[1 - CDF[BinomialDistribution[#, 0.20], 4] >= 0.90, #, # + 1] &, 1] Out[26]= 38 -- Andrzej Kozlowski Toyama International University Toyama, Japan http://sigma.tuins.ac.jp/