设(X_(1),X_(2),X_(3),X_(4))是总体X的简单随机样本,X~N(0,4),F=C(X_(1)^2)/(X_(2)^2+X_{3)^2+X_(
7.设X_(1),X_(2),X_(3)是来自总体Xsim N(0,1)的一组样本,则X_(1)+X_(2)+X_(3):____,X_(1)^2+X_(2)^
3.(填空题)3.设X_(1),...,X_(5)是来自总体X的样本,且Xsim N(0,1),则k=____时,kcdot(X_(1)^2+X_(2)^2+X
X_(n)是取自总体N(0,1)的样本,则X^2=X_(1)^2+X_(2)^2+X_(3)^2simchi^2(_).5.设$X_{1},X_{2},\cdo
设X_(1),X_(2),...,X_(n)为总体Xsim N(mu,sigma^2)的样本,证明hat(mu)_(1)=(1)/(2)X_(1)+(2)/(3
X_(8)是来自正态总体Xsim N(0,9)的样本,证明:(X_(1)+X_(2)+X_(3)+X_(4))/(sqrt(X_(5)^2)+X_{6^2+X_
已知随机变量X_(1), X_(2), X_(3)的协方差COV(X_(1), X_(3)) = 2, COV(X_(2), X_(3)) = 1。则COV(X
二次型f(x_(1),x_(2),x_(3))=2x_(1)^2+x_(2)^2-4x_(3)^2-4x_(1)x_(2)-2x_(2)x_(3)的标准型为(
22 (1)设随机变量X_(1),X_(2),X_(3),X_(4)相互独立,且有E(X_(i))=i,D(X_(i))=5-i,i=1,2,3,4.设Y=2X
5、设总体Xsim N(mu,sigma^2),x_(1),x_(2),x_(3)为来自X的样本,则当常数a=____时,hat(mu)=(1)/(4)x_(1