得 P(Z=r)=∑P(X=i,Y=r-) i=0 0 (r- e) e(t2) (2+22),r=0,1,2, 即Z服从参数为入+2的泊松分布。= = = = = − r i P Z r P X i Y r i 0 ( ) ( , ) 得 = = r i 0 r-i - 2 i - 1 (r -i)! e i! e 1 2 = − + = r r i e 0 r-i 2 i 1 ( ) i!(r -i)! r! ! 1 2 ( ) , 0,1,2, . ! 1 2 ( ) 1 2 = + = − + r r e r 即Z服从参数为 的泊松分布。 1 + 2