I am trying to find the MLE of the following functions but I'm getting stuck. I know the method and steps to follow but Pi notation is confusing for me.
1) f(x) = øx^(ø-1), 0 < x < 1 and 0 < ∞. Let X1, X2, ... Xn be a random sample. What is the MLE of ø?
So I can get it into pi notation as multiple from i=1 to n, øxi^(ø-1). I figured I can pull out a ø^n, but I'm stuck after that. Is there some type of trick here?
2) f(x) = (1/ø)x^((1-ø)/ø), 0 < x < 1 and 0 < ∞. Let X1, X2, ... Xn be a random sample. What is the MLE of ø?
I'm not even sure how to approach this one. How can I get this into a sensible form?