Convergence Concepts in Probability
A short note on almost sure convergence, convergence in probability, convergence in distribution, convergence in mean, and the relationships between these modes of convergence.
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Academic Notes · Probability
Probability Theory
Notes on probability spaces, random variables, expectation, conditional expectation, independence, convergence, laws of large numbers, and central limit theorems.
Probability Theory
Notes and drafts.
This section collects foundational notes in probability theory, emphasizing concepts that recur in asymptotic statistics, stochastic modelling, machine learning theory, and decision-making under uncertainty.
Conditional Expectation as Projection
A conceptual note on conditional expectation, sigma-algebras, measurability, and the Hilbert-space projection interpretation.
Coming soonLaws of Large Numbers
A note comparing weak and strong laws of large numbers, with examples showing why averaging stabilizes random quantities.
Coming soonCentral Limit Theorems
A note on classical central limit theorems, asymptotic normality, normalization, and their role in statistical inference.
Coming soon