总体X~N(μ,σ), X1, X2…, X10是来自X的样本答:解析:设总体X~N(μ,σ2),X1,X2,…,X10是来自X的样本。设总体X~N(μ,σ2),X1,X2,…,X10是来自X的样本。解:因为X~N(μ,σ^2),而X1,X2…X10是取自总体X的样本,所以有Xi~N(μ,σ^2),即f(xi)=1/√(2πσ) e^ [-(xi-μ)^2/2σ^2] (i=1,2,…...
总体X~N(μ,σ^2),有样本X1,X2,…Xn,设Y=0.5(Xn-X1),则Y~___.答:总体X~N(μ,σ^2),有样本X1,X2,…Xn,设Y=0.5(Xn-X1),则Y~___. X~N(0,σ^2)E(X1+X2)=EX1+EX2=0D(X1+X2)=DX1+DX2=2σ^2X1+X2~N(0,2σ^2)同理:X1-X2~N(0,2σ^2)所以1/√2σ(X1+X2)~N(0,1)1/√2σ(X1-X2)~N(0,1)所以1/2σ^2(X1+X2)^2~...
总体X~N(μ,σ^2),有样本X1,X2,…Xn,设Y=0.5(Xn-X1),则Y~___.答:X~N(0,σ^2)E(X1+X2)=EX1+EX2=0D(X1+X2)=DX1+DX2=2σ^2X1+X2~N(0,2σ^2)同理:X1-X2~N(0,2σ^2)所以1/√2σ(X1+X2)~N(0,1)1/√2σ(X1-X2)~N(0,1)所以1/2σ^2(X1+X2)^2~X^2(1)X^2(n)代表自由度为n的卡方分布同理1/2σ^2(X1-X2)^2~X^2(...