单选题
Given the conditional probabilities in the table below and the unconditional probabilities P(Y=1)=0.4 and P(Y=2)=0.6, what is the expected value of X?
| x i | P(x i |Y=1) | P(x i |Y=2) |
| 3 | 0.7 | 0.2 |
| 4 | 0.3 | 0.8 |
【正确答案】
C
【答案解析】[解析] P(X=3，Y=1)=P(X=3|Y=1)×P(Y=1)=0.7×0.4=0.28
P(X=4，Y=1)=P(X=4|Y=1)×P(Y=1)=0.3×0.4=0.12
P(X=3，Y=2)=P(X=3|Y=2)×P(Y=2)=0.2×0.6=0.12
P(X=4，Y=2)=P(X=4|Y=2)×P(Y=2)=0.8×0.6=0.48
从而得到联合概率表如下表所示。
P(X=4，Y=1)=P(X=4|Y=1)×P(Y=1)=0.3×0.4=0.12
P(X=3，Y=2)=P(X=3|Y=2)×P(Y=2)=0.2×0.6=0.12
P(X=4，Y=2)=P(X=4|Y=2)×P(Y=2)=0.8×0.6=0.48
从而得到联合概率表如下表所示。