Maximum Likelihood Estimate

[macro90]

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

http://www.sosmath.com/CBB/latexrender/pictures/c3ceb387cd3cb89f045cc4503749703a.gif

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?

http://www.geocities.com/ketthianorak/rbahonvac/pride-iq/philip-atkinson.png
http://www.geocities.com/ketthianorak/rbahonvac/pride-iq/is-a-bitter-old-loser.png

[quark]

Hi Macro90,

I think your procedure is correct. Note (1+theta)^112 * (1-theta)^31 does not equal (1+theta)^143 :)

[JohnM]

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

:D

[macro90]

yes, you're right.. I can't believe I didn't see that.

[quark]

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...