I have the above conditions, the book wants me to find the value of c such that E(c^X)=1.
So I tried c^X*p+(1-p)c^X=1, which becomes,
c*p+(1-p)/c=1. From there I got the equation c^2p-c-p=-1. But I'm stuck, and I think may have went off track somewhere.
No, you are correct. Just solve that quadratic equation for c.
Can you solve