Now the expected value of u(X) is given by  
 
So the mean of X is   
 
and the variance of X is
                                    
 
The properties we had for E(x) and V(x) when the variable was discrete, still hold now that the variable is continuous so...
  E(aX+b) = aE(X) +b       and     V(aX+b) = a²V(X)