STAT 135 Lecture Notes - Lecture 7: Maximum Likelihood Estimation, Likelihood Function, Xz
Quiz IThursday
2problems
similar to HW ILun starred problems )
30 min
will Provide summary sheet of distribution
Today :1) Intro to ME
27 Properties of MLE
3) review x2 ,adist
4) CI for MLET for µ,Fof NCMTY
generally
section 8.5 Maximum likelihood estimate CULE )
suppose the RVs Xi ,Xz . -.Xn have Ajoint density
f(Xi ,Xz . ..Xnlf )
Given observed values ,X=X ,,Xz=X2 ,
.--
Xn÷
we form likelihood function fixed
likcotfcxixz
---Xnlo )←function of 0,Xfixed
The Max value of likcf )represents the value on athat
maximizes the likelihood of us Observing our data
If Xi are i. i. d
lik Co)=#,fcxilo )
Rather than maximize like )we maximize its
log Llog is monotonically increasing )
dlo )=bog likelihood =fngbogcfcxilo))
TO maximize lco )we take the derivative set equal
to zero and solve for -0
find Em¥ is asit .l'
107=0
