# Maximum Entropy Principle The maximum entropy principle selects the probability distribution that is "least biased" given known constraints—it maximizes entropy while satisfying the constraints, making no additional assumptions beyond what's required. Lagrange multipliers are used to solve the constrained optimization problem of maximizing entropy subject to the given constraints. For example, the [[Gaussian Distribution]] has maximum entropy among all distributions with: (1) support on the entire real line, (2) fixed mean, and (3) fixed variance.