Question

b(1,0.3),u(-1,1),记z=x+y.求z的概率密度函数

Answer 1

P(Z=-1)=P(X+Y=-1)=P(X=0)*P(Y=-1)=0.7*(1/3)=7/30

P(Z=0)=P(X+Y=0)=P(X=0)*P(Y=0)+P(X=1)*P(Y=-1)=0.7*(1/3)+0.3(1/3)=1/3

P(Z=1)=P(X+Y=1)=P(X=1)*P(Y=0)+P(X=0)*P(Y=1)=0.3*(1/3)+0.7*(1/3)=1/3

P(Z=2)=P(X+Y=2)=P(X=1)*P(Y=1)=0.3*(1/3)=1/30