[Verse 1] In probability spaces we begin to see Random variables dancing wild and free Expectation values guide us to the mean Law of large numbers makes the pattern clean Central limit shows us normal curves arise From any distribution to our surprise [Chorus] Probability and stats will light the way From random walks to Bayes we learn each day Markov chains and Brownian motion flow Information theory helps our knowledge grow Measure theory deep, statistics strong This is our probability song [Verse 2] Stochastic processes march through time and space Markov chains remember just the present place Poisson counting random events that arrive Martingales keep fair games alive Brownian particles wander left and right Mathematical models burning bright [Chorus] Probability and stats will light the way From random walks to Bayes we learn each day Markov chains and Brownian motion flow Information theory helps our knowledge grow Measure theory deep, statistics strong This is our probability song [Verse 3] Statistical theory puts data to the test Maximum likelihood gives estimates best Hypothesis testing with p-values small Sufficient statistics capture it all Confidence intervals bracket what we seek Making bold inferences from samples weak [Bridge] Bayesian thinking flips the script around Prior beliefs with evidence are found Posterior updates as new data flows MCMC sampling when the integral grows Conjugate families make computation clean The most elegant math you've ever seen [Verse 4] Stochastic calculus takes us to the edge Ito integrals fulfill the pledge Differential equations driven by noise Feynman-Kac gives us modeling choice Information measured by entropy's rule Shannon's theorems are the coding tool [Verse 5] High dimensions bring us concentration Random matrices need investigation Sparse recovery finds the signal true Ergodic theory with measure preserving too Transformations mixing through the space Mathematical beauty shows its face [Outro] From coin flips simple to equations deep These are the patterns that we'll always keep Probability and statistics reign supreme In the mathematical learning dream
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