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#1
11-02-2006, 03:19 AM
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Standard Deviation
What is the Std Dev of a series of random coin flips?
http://www.agribiz.com/merchdiz/cointoss/cointoss.html 
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#2
11-02-2006, 03:49 AM
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Re: Standard Deviation
[ QUOTE ]
What is the Std Dev of a series of random coin flips? http://www.agribiz.com/merchdiz/cointoss/cointoss.html [/ QUOTE ] The standard deviation of the number of heads in N flips of a fair coin is sqrt(N)/2. Proof: Let X be a random variable that takes the value +1 on a head, and 0 on a tail. E(X) = (1/2)*1 + (1/2)*0 = 1/2 Var(X) = E(X^2) - [E(X)]^2 = (1/2)*1^2 + (1/2)*0^2 - (1/2)^2 = 1/4 The variance of X for N flips is N*Var(X) = N/4. The standard deviation for N flips is sqrt(N/4) = sqrt(N)/2. This is the standard deviation of a binomial distribution with p = 1/2. The standard deviation of a general binomial distribution is sqrt[N*p*(1-p)], which we can derive the same way as above. For p = 1/2, this is sqrt[N*(1/2)*(1/2)] = sqrt(N/4) = sqrt(N)/2.
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#3
11-02-2006, 05:03 AM
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Re: Standard Deviation
[ QUOTE ]
[ QUOTE ] What is the Std Dev of a series of random coin flips? http://www.agribiz.com/merchdiz/cointoss/cointoss.html [/ QUOTE ] The standard deviation of the number of heads in N flips of a fair coin is sqrt(N)/2. Proof: Let X be a random variable that takes the value +1 on a head, and 0 on a tail. E(X) = (1/2)*1 + (1/2)*0 = 1/2 Var(X) = E(X^2) - [E(X)]^2 = (1/2)*1^2 + (1/2)*0^2 - (1/2)^2 = 1/4 The variance of X for N flips is N*Var(X) = N/4. The standard deviation for N flips is sqrt(N/4) = sqrt(N)/2. This is the standard deviation of a binomial distribution with p = 1/2. The standard deviation of a general binomial distribution is sqrt[N*p*(1-p)], which we can derive the same way as above. For p = 1/2, this is sqrt[N*(1/2)*(1/2)] = sqrt(N/4) = sqrt(N)/2. [/ QUOTE ] I'm probably using the formula incorrectly, but if I flip a coin 100k times I get Std Dev = 158. If I flip it 1mm times I get Std Dev = 500 This doesn't make sense.
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#4
11-02-2006, 05:22 AM
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Re: Standard Deviation
[ QUOTE ]
I'm probably using the formula incorrectly, but if I flip a coin 100k times I get Std Dev = 158. If I flip it 1mm times I get Std Dev = 500 This doesn't make sense. [/ QUOTE ] That's correct. A million is 10 times greater than 100K, so the standard deviation will be sqrt(10) times greater. Why do you think it doesn't make sense?
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#5
11-02-2006, 05:28 AM
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Re: Standard Deviation
[ QUOTE ]
[ QUOTE ] I'm probably using the formula incorrectly, but if I flip a coin 100k times I get Std Dev = 158. If I flip it 1mm times I get Std Dev = 500 This doesn't make sense. [/ QUOTE ] That's correct. A million is 10 times greater than 100K, so the standard deviation will be sqrt(10) times greater. Why do you think it doesn't make sense? [/ QUOTE ] Ah. I understand. When I look at the STD DEV in my pokertracker stats, it is per hour or per 100 hands. That's the problem What would the STD DEV be per 100 flips?
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