1. The problem statement, all variables and given/known data f(x;theta)=Exp(-x+theta) Find parameter estimates for variable 'theta' using maximum likelihood Estimator and Method of Moments. 2. Relevant equations Log(x; theta) = Log(Exp(-x + theta)) -- For MLE Integral from theta to infinity of (x*Exp(-x + theta)) = xbar -- For Method of Moments 3. The attempt at a solution I evaluate the log-likelihood function to get Log(L)= -x + theta and then take the derivative of the log-likelihood function with respect to theta. The problem here arises when I take this derivative and set it equal to zero since it gives me 0 = 1 with none of my parameters left in the equation. In performing the method of moments analysis i get that the estimation for theta is equal to the xbar + 1. Don't know if this is correct, but if someone could help me see what I'm doing wrong with either of these parts it would be most appreciated.