The definition of Expected Value in the first course in probability by Sheldon Rosss is defined as
$$E[X] = \sum_{x:p(x)\gt0} xp(x)$$
where the negative outputs of PMF is ignored in calculating the expectaion.
I saw the following in a different book where they are considering the negative value while calculation expectation.
If P(W=−3)=0.2, and P(W=−11)=0.7, andP(W=31)=0.1.
Then E(W)=(−3)(0.2)+(−11)(0.7)+(31)(0.1)=−0.6−7.7+3.1=−5.2.
In this case, the expected value of W is negative.
Is my interpretation of the formula incorrect ?