【正确答案】正确答案:(Ⅰ)(X
1
,X
2
)是二维离散型随机变量,其可能的取值为(0,0),(0,1),(1,0),(1,1)。 当(X
1
,X
2
)=(0,0)时,说明随机抽取的一件不是一等品,也不是二等品,则必为三等品,故F{X
1
=0,X
2
=0}=P{X
3
=1}=0.1。 类似地P{X
1
=0,X
2
=1}=P{X
2
=1}=0.1, P{X
1
=1,X
2
=0}=P{X
1
=1}=0.8, P{X
1
=1,X
2
=1}=

=0, 故X
1
与X
2
的联合分布:

(Ⅱ)由(Ⅰ)知,X
1
和X
2
的边缘分布均为0—1分布。由0—1分布的期望和方差公式得 E(X
1
)=P{X
1
=1}=0.8,D(X
1
)=P{X
1
=1}P{X
1
=0}=0.8×0.2=0.16, E(X
2
)=P{X
2
=1}=0.1,D(X
2
)=P{X
2
=1}P{X
2
=0}=0.1×0.9=0.09, E(X
1
X
2
)=0×0×0.1+0×1×0.1+1×0×0.8+1×1×0=0, Cov(X
1
,X
2
)=E(X
1
X
2
)一E(X
1
)E(X
2
)=一0.08, 则相关系数
