E(X)=1*p+(-1)*(1-p)

Solution for E(X)=1*p+(-1)*(1-p) equation:

(E)=1E+(-1)(1-E)

We move all terms to the left:

(E)-(1E+(-1)(1-E))=0

We add all the numbers together, and all the variables

E-(1E+(-1)(-1E+1))=0

We multiply parentheses ..

E-(1E+(+E-1))=0


We calculate terms in parentheses: -(1E+(+E-1)), so:

1E+(+E-1)

We add all the numbers together, and all the variables

1E+(E-1)

We add all the numbers together, and all the variables

E+(E-1)

We get rid of parentheses

E+E-1

We add all the numbers together, and all the variables

2E-1

Back to the equation:

-(2E-1)


We get rid of parentheses

E-2E+1=0

We add all the numbers together, and all the variables

-1E+1=0

We move all terms containing E to the left, all other terms to the right

-E=-1

E=-1/-1

E=1