Maximum Likelihood Estimate

I need to find the ML-estimate of theta. The likelihood function I got is

To get the ML-estimate, I believe I need to simplify, take logs, derive with respects to theta, and then equate with zero to find the the value of theta that maximizes L(theta). My working out is below. I think I have made a mistake beacuse I'm not sure if I'm supposed to get a negative number. Have I done it right?



TS Contributor
Like they say in calculus and statistics, it's not the calculus or statistics that gets you, it's the algebra.....

It happened to me all the time. The nice thing about statistics is if there is something wrong the results often do not make sense, eg. a negative probability, so you can go back and check...