Stats - Binomial Distribution mean and stdev

fish

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.

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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.

霏

                               
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fish

原帖由 幻將 於 8/3/2008 11:21 PM 發表

                               
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找到一本舊書.....
μ是個RV
D是 Variance function
改一改notation及綜合兩者的answer就行了, 謝=]

                               
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reference: Gnedenko,"Part 28 Theory of Expectation and Variance" ,Theory of Probability