Articles by tag: probability-theory

GPT-5.4 Pro: counterexample to GCI for non-centered measures

GPT-5.4 Pro disproved the hypothesis of the Gaussian correlation inequality for shifted Gaussian measures. Counterexample in 2D with strips, generalization to n≥2. Solution details on solveall.org. Study for AI in mathematics.

Moment Generating Function: formulas and properties

Study the moment generating function for computing moments of distributions. Taylor series expansion, properties for sums, example with exponential distribution. For developers and data science analysts.