单选题
18.假设X是只有两个可能值的离散型随机变量，y是连续型随机变量，且X和y相互独立，则随机变量X+Y的分布函数( )．
【正确答案】
C
【答案解析】不妨设X的分布律为P(X=ai)=pi，i=1，2，Y的密度函数为g(y)．下面求X+Y的分布函数
FZ(z)=P(X+Y≤z)
=P{(X+Y≤z)∩[(X=a1)∪(X=a2)]}
=P[(X+y≤z，X=a1)U(X+Y≤z，X=a2)]
=P(X+Y≤z，X=a1)+P(X+y≤z，X=a2)
=P(y≤z一a1，X=a1)+P(Y≤z一a2，X=2)
=P(Y≤z一a1)P(X=a1)+P(y≤z一a2)P(X=a2)
=
FZ(z)=P(X+Y≤z)
=P{(X+Y≤z)∩[(X=a1)∪(X=a2)]}
=P[(X+y≤z，X=a1)U(X+Y≤z，X=a2)]
=P(X+Y≤z，X=a1)+P(X+y≤z，X=a2)
=P(y≤z一a1，X=a1)+P(Y≤z一a2，X=2)
=P(Y≤z一a1)P(X=a1)+P(y≤z一a2)P(X=a2)
=