Homework Statement
Let a function f : R => R be convex. Show that f is necessarily continuous. Hence, there can be no convex functions that are not also continuous.
Homework Equations
The Attempt at a Solution
F is continuos if there exist \epsilon >0 and \delta>0 such that |x-y|<...
ugh, yea that was obvious! :) well thanks again! it help me a lot! i can already see that i'll have more questions for this class, well let's wait for next hw...
I thought that I get it, but hm, I didn't. Well I thought that I am supposed to find p_i's at which is this function maximized. Because problem says that I don't have a control over x's or n?
So I understand what you said in your last reply, but is that my final answer then?
ok, so this is what I have so far:
on the right hand side when I differentiate constraint I get just \lambda, for every p.
But I still didn't figured out how to diff the function. So I have something like
log (n!/x1!...xk!) p1^x1 p2^xk is the same as
log (n!/x1!...xk!) + log p1^x1 +...
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, \Sigma xi=n, 0 <pi <1, and \Sigma pi=1
The maximum...