Prove that the following function is convex over the set of positive vectors: f(x1, x2, x3) = -√√x₁x2 + 2x² + 2x² + 3x² − 2x1x2 − 2x2x3 - -

find deriventine (9).5"(

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Hamilton County Judges Reporter Kristen DelGuzzi of The Cincinnati Enquirer is writing a piece about the effectiveness of judges in Hamilton County, Ohio. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed, some of the cases are reversed. Over a three-year period the Hamilton County Common Pleas Court, Domestic Relations Court, and Municipal Court handled 182,908 cases. The purpose of the newspaper's study is to evaluate the performance of each court and the judges who render their decisions. Appeals are often the result of mistakes made by judges, and the newspaper wanted to know which court and which judges were doing a good job and which were making too many mistakes. You have been hired to assist in the data analysis at the court level (judge-level analysis will be done at a later time). You must use your knowledge of probability and conditional probability to help determine the likelihood of…