Discrete Random Variable 11/6

The Expected value of a random variable X with probability mass m is defined as:

$$E[X]=\sum_{x:m(x)>0}x . m(x)$$

Example of the dice game:
Say you lose the points marked for an odd number, win the points marked for an even one. What is your expected gain?

$$E[X]=\frac{1}{6}\times(-1)+ \frac{1}{6}\times(+2)+ \frac{1}{... ...6}\times(+4)+ \frac{1}{6}\times(-5) + \frac{1}{6}\times(+6)=0.5$$