I am reading the article Deriving probability distributions using the Principle of Maximum Entropy and trying to derive some of the equations in it automatically using Mathematica.
I want to solve the system of equations below automatically.
$$ 1+\text{ln} p(x)-\lambda_0=0 $$ $$ \int_a^b p(x) dx=1 $$
My code is
Solve[1 - λ0 + Log[p[x]] == 0 &&
Integrate[p[x], {x, -Infinity, Infinity}] == 1 , {p[x], λ0} ]
But I get the error output,
Solve: This system cannot be solved with the methods available to Solve.
What should I do to make Mathematica able to solve the above system of equations?