Let X be a continuous random variable with cdf F(x). Let ξ_1/2 denote the
median of F(x). Suppose X_1, X_2, ,,,, X_n is a random sample from the
distribution of X with corresponding order statistics Y_1 < Y_2 <...<Y_n.
As before, let Q_2 denote the sample mean which is an point estimator of
ξ_1/2. Select α, so that 0 < α < 1. Take c_α/2 to be the α/2th quantile
of a binomial b(n,1/2) distribution; that is, P[S≦c_α/2] = α/2, where S
is distributed b(n,1/2). Then note also that P[S≧n-c_α/2] = α/2. Thus it
follows from expression(*) that P[Y_[(c_α/2)+1] < ξ_1/2 < Y_(n-c_α/2)] =
1-α.
j-1
P[Y_i < ξ_p < Y_j] = Σ C(n,w) p^w (1-p)^(n-w) ......(*)
w = i
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不瞭解為什麼由(*)可以推得P[Y_[(c_α/2)+1] < ξ_1/2 < Y_(n-c_α/2)] = 1-α？
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