Variance Reduction Techniques: Antithetic Variables & Importance Sampling

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Covers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.

Explores PDFs and CDFs for discrete and continuous random variables, including Gaussian, uniform, and exponential distributions.

Covers fundamental concepts in probability and statistics, including distributions, properties, and expectations of random variables.

Explores joint random variables, conditional density, and independence in probability and statistics.

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Covers the estimation of random variables, including expectations, variances, and quantiles.

Explores continuous random variables, cdf, pdf, convolution, and sum of dice.

Explores quantiles, sampling, and histogram density for understanding distributions and constructing confidence intervals.

Covers the modes of convergence of random variables and the Central Limit Theorem, discussing implications and approximations.

Introduces probability theory, random variables, and distributions, with a focus on their applications in atomic diffusion.