Pareto distribution

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Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Explores Gaussian vectors, moment generating functions, independence, density functions, affine transformations, and quadratic forms.

Covers ECDF, quantiles, mean, median, and box plots for dataset analysis.

Covers the Metropolis-Hastings algorithm and gradient-based approaches for biasing searches towards higher likelihood values.

Explores variance reduction techniques like antithetic variables and importance sampling in Monte Carlo estimation.

Covers the exponential family of distributions and the Ising model, explaining magnetism through dipoles and spins.

Covers Green's representation formula, fundamental solutions, and distribution properties.

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Explores proof ideas related to the cut-off phenomenon and its implications in random walks on hypercubes.

Discusses mutual information, data processing inequality, and properties related to leakage in discrete systems.