Answer:-
The distribution that maximizes the quadratic score is the true probability distribution of the outcomes. The quadratic score, also known as the Brier score, measures the accuracy of probabilistic predictions by comparing predicted probabilities with actual outcomes. It rewards predictions that are closer to the true probabilities and penalizes those that deviate. To maximize the score, your predicted probabilities must align perfectly with the actual likelihood of each outcome. In practice, this means accurately estimating the true distribution based on available data and ensuring predictions reflect reality as closely as possible. Accurate, well-calibrated predictions lead to the best scores.
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