Moments and the Alike

Let \((\Omega ,\mathcal {F})\) be an event space representing the following random experiment: a gamble s.t. you win € 1000 with probability \(p>0\) and you loose € 900 with probability \(1-p\) . How much you wish to get a gain or you fear to suffer a loss, from this gamble on average? First, we can define the discrete rv X having distribution with masses \(\mathsf {P}(X=1000)=p\) and \(\mathsf {P}(X=-900)=1-p\) .