I have to find likelihood and log-likelihood functions of Weibull distribution:
$$f(x)=\alpha(\beta)^{-\alpha}x^{\alpha-1}e^{-(\frac{\alpha}{\beta})^\alpha}$$
However, I am given a restriction of $E(X)=1$, which makes $\beta$ a funtion of $\alpha$. How to interpret this restriction and what does it exactly mean when calculating likelihood functions?