由题意知，：Y = X²的所有可能取值为0, 1，4, 9。相应的概率为:

P(Y =0) =P(X=0) =1/5

P(Y=1)=P（X² =1) = P(X = 1) + P(X = -1) =1/15 +1/6 =7/30

P(Y = 4) =P(X= -2) =1/5

P(Y = 9) =P(X = 3) =11/30

故Y的概率分布列为：