Suppose that $Y_1,Y_2,...,Y_n$ are a sample of size $n$ and IID, each of which have distribution
$f_Y(y)=\frac{2y}{\theta^2}$ with support $0<y<\theta$
Find the MLE (method of maximum likelihood) estimate of $\theta$.
I decided to use the log-likelihood technique, but after taking the derivative I end up with this equation:
$$\frac{-2n}{\theta}\sum_{i=1}^nln(Y_i)=0$$
So this suggests that there is no value of $\theta$ that acts as an MLE estimate... but I'm not sure if there are other approaches or if I've made a mistake. How would you find the MLE estimate of $\theta$?