- #1
Legendre
- 62
- 0
Homework Statement
L = - [itex]\Sigma[/itex] x,y (P(x,y) log P(x,y)) + [tex]\lambda[/tex] [itex]\Sigma[/itex]y (P(x,y) - q(x))
This is the Lagrangian. I need to maximize the first term in the sum with respect to P(x,y), subject to the constraint in the second term.
The first term is a sum over all possible values of x,y.
The second term is a sum over all possible values of ONLY y.
Homework Equations
Given above.
The Attempt at a Solution
I know I have to differentiate L with respect to P(x',y') where x',y' are fixed values.
The idea is that the first term consists of a sum of P(x,y) over all possible x,y. So, we just need to differentiate L with respect to P(x',y') while keeping all other P(x,y) constant.
But how do I differentiate the second term with respect to P(x',y')? It is a sum over all possible y values.
I know the solution is supposed to be [tex]\lambda[/tex] when the second term is differentiated with respect to a particular P(x',y') but how do we obtain that?
THANKS! :)
Last edited: