Two persons $A$ and $B$ play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even, A will get $\frac{1}{2}$ point and $B$ will get $\frac{1}{2}$ point.

If the sum is odd, A will get one point and $B$ will get no point. The arithmetic mean of the random variable of the number of points of $A$ is