I put that on my exam last week. you need the likelihood function, which is
you can differentiate this or take the log and differentiate that.
NOW differentiate and set equal to zero.
Hi, I'm trying to solve the following problem:
Let Y1, Y2, ..., Yn denote a random sample from the probability density function
, for
and 0 elsewhere.
Find the MLE for . Compare the answer to the method-of-moments answer: [2(Y bar) -1]/[1-(Y bar)
Sorry for that last part. Y bar means Y with the line on top.
I tried to do this by taking the lns of each term after multiplying the fy's, taking the derivative with respect to theta, and equating to zero but I end up with - (ln y + 1). Is this possible? I figure it's not since it asks to compare to the M.O.M. answer which seems totally different...
Any ideas?
I put that on my exam last week. you need the likelihood function, which is
you can differentiate this or take the log and differentiate that.
NOW differentiate and set equal to zero.
Ohhhh right... Forgot about that log rule... I know once I take the derivative I get:
and that I'm supposed to get (Y bar) from the summation on the right side but how can I get rid of that ln? Because if I take the exp of both sides I'll end up with theta as a exponent... If I put n ln and then I won't get (Y bar) like I want... and it just occured to me that doesn't even make sense..