设随机变量X1，X2，…，Xn（n＞1）独立同分布，且方差σ2＞0．令随机变量Y=1nni=1Xi，则（　　）A．D(X1+

2025-04-14 04:22:34

推荐回答（1个）

回答1：

由于随机变量X₁，X₂，…，X_n（n＞1）独立同分布，
于是可得：
COV（X，Y）=COV（X1，

/picurl?url=https%3A%2F%2Fiknow-pic.cdn.bcebos.com%2F203fb80e7bec54e754c734a9ba389b504fc26a59%3Fx-bce-process%3Dimage%2Fquality%2Cq_85

i=1

Xi）=

COV(X1，

/picurl?url=https%3A%2F%2Fiknow-pic.cdn.bcebos.com%2F203fb80e7bec54e754c734a9ba389b504fc26a59%3Fx-bce-process%3Dimage%2Fquality%2Cq_85

i=1

Xi)=

/picurl?url=https%3A%2F%2Fiknow-pic.cdn.bcebos.com%2F203fb80e7bec54e754c734a9ba389b504fc26a59%3Fx-bce-process%3Dimage%2Fquality%2Cq_85

i=1

COV(X1，Xi)
=

COV(X1，X1)=

D(X1)=

σ2．
故答案选：C．