show that μ=np and σ=sqrt(npq) in a binomial distrubution. (Bernoulli trail) where μ = mean n = number of sample p = probability of sucess
σ = standard deviation q = probability of failure ( i.e. q = 1-p )
The answer in wiki is just for 0 and 1 and I don't know if it is possible and how to use MI to proof the above two functions are applicable to every number.
The hint is using μ=sum of data/ number of data and σ = sqrt(variance)
It is required to use MI but I couldn't think of the answer using substitution many times.
----------------------------------------------------------------------------- Let a and b are the two outcomes where a = success
p = P(a) q = P(b)
pq = var/ n
And then I just got stuck with the sigma notation for variance. Similar thing happens to the mean also.
發表於 8/3/2008 02:01 AM 
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