- #1
shotputer
- 11
- 0
Lagrange mult. ---finding max
Homework Statement [/b]
probability mass function is given by
p(x1,...,xk; n, p1,... pk) := log (n!/x1!...xk!) p1^x1 p2^xk
Here, n is a fixed strictly positive integer, xi E Z+ for 1 < i < k, [tex]\Sigma[/tex] xi=n, 0 <pi <1, and [tex]\Sigma[/tex] pi=1
The maximum log-likelihood estimation problem is to find:
arg max log p(x1,...,xk; n; p1...pk)
over all possible choices of (p1 ...pk) E Rk such that
[tex]\Sigma[/tex] p i=1
(Hint: You have no control over x1,...,xk
or n and may regard them as given.)
Well I know that I need to find first derivative of function p, and of function "g"- constraint, but I don't know where, or how to actually start...
Please help, thank you
Homework Statement [/b]
probability mass function is given by
p(x1,...,xk; n, p1,... pk) := log (n!/x1!...xk!) p1^x1 p2^xk
Here, n is a fixed strictly positive integer, xi E Z+ for 1 < i < k, [tex]\Sigma[/tex] xi=n, 0 <pi <1, and [tex]\Sigma[/tex] pi=1
The maximum log-likelihood estimation problem is to find:
arg max log p(x1,...,xk; n; p1...pk)
over all possible choices of (p1 ...pk) E Rk such that
[tex]\Sigma[/tex] p i=1
(Hint: You have no control over x1,...,xk
or n and may regard them as given.)
Homework Equations
The Attempt at a Solution
Well I know that I need to find first derivative of function p, and of function "g"- constraint, but I don't know where, or how to actually start...
Please help, thank you