母分散の計算

最近変動性の計算式の由来を考えていました。特に標本の変動性と母分散の関係を見直しています。自分の推測は(1/n)sigma(i=1 to n)*1sigma(i=1 to n)*2*sigmas^2
, where
sigmas^2
is the sample variance.

*1:xi-mu)^2) ですが教科書には 「(1/(n-1

*2:xi-mu)^2)」 と書いてあります。 The derivation, although lengthy, is a straightforward calculation of the expectation of the variance E(sigma^2) in terms of the sample variance, (1/n)sigma((x-mu)^2) . The complicated aspect is that the variance itself is an expectation, so the usual sum of the probability times (x-mu)^2 is computed, substituting sigma(x) for mu, and then the outer expectation is moved inside the summation to apply to the xi terms. 結局計算式が単純化されるし E(sigma^2) = (n/(n-1