∵Eξ= 7 6 =0×a+1× 1 3 +2× 1 6 +3b∴b= 1 6 ,∵P(ξ=0)+P(ξ=1)+P(ξ=2)+P(ξ=3)=1∴a+ 1 3 + 1 6 + 1 6 =1∴a= 1 3 .故答案为: 1 3