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Explore the cosmological applications of the Gamma-Ray Bursts fundamental plane relation combined with Type Ia Supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO), and Quasars in this one-hour lecture. Delve into the challenges of precision cosmology, examining the assumption of Gaussianity in distance moduli likelihood and its impact on cosmological parameter constraints. Discover how applying new likelihood distributions, such as logistic and Student's t, to the Pantheon and Pantheon+ SNe Ia data significantly reduces uncertainties in matter density and Hubble constant measurements. Investigate the implications of these findings on the Hubble tension and the combined use of Gamma-Ray Bursts, Quasars, and BAO in cosmological studies. Learn about the Dainotti 3D relation, the tightest GRB correlation in literature, and its application with evolution correction in the platinum sample.