Advanced Statistics

Deep dive into probability, distributions, and hypothesis testing.

Set Theory, Sample Spaces, and Events
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11 min
Axioms of Probability (Kolmogorov)
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5 min
Conditional Probability and Independence
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17 min
Law of Total Probability and Bayes' Theorem
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16 min
Probability Mass Functions (PMF) and Cumulative Distribution Functions (CDF)
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12 min
Expected Value E[X], Variance Var[X], and Standard Deviation
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18 min
Common Discrete Distributions (Binomial, Poisson, Geometric)
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8 min
Moment Generating Functions (MGFs) for Discrete R.V.s
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9 min
Probability Density Functions (PDF) and CDF
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13 min
Expected Value and Variance via Integration
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14 min
Common Continuous Distributions (Uniform, Exponential, Gamma)
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8 min
MGFs for Continuous R.V.s
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18 min
Joint PMFs and Joint PDFs
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12 min
Marginal and Conditional Distributions
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10 min
Covariance Cov(X, Y) and Correlation ρ
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5 min
Independence of Random Variables
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13 min