Common Probability Distributions

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Lyrics

[Verse 1]
Picture data scattered wide, each point the same
No peaks or valleys hiding, uniform's the name
Stocks within a trading range, bounded left and right
Every outcome just as likely, probabilities unite
When minimum and maximum frame your world complete
Rectangle distributions make the math so neat

[Chorus]
Uniform, binomial, normal curves we trace
Each distribution finds its financial place
Flat or binary, bell-shaped destiny
Master these three patterns, unlock what markets see
Distribution nation, probability's foundation

[Verse 2]
Success or failure calling, binary the game
Coin flips and bond defaults share binomial's claim
Count the wins from trials, fixed attempts you make
Portfolio components that can break or never break
Independence matters, probability stays true
Ten percent default rate guides what banks pursue

[Chorus]
Uniform, binomial, normal curves we trace
Each distribution finds its financial place
Flat or binary, bell-shaped destiny
Master these three patterns, unlock what markets see
Distribution nation, probability's foundation

[Bridge]
Bell curve reigns supreme in finance halls
Stock returns and errors heed its calls
Sixty-eight percent within one standard measure
Ninety-five in two, asymptotic treasure
Central limit theorem brings convergence near
When sample sizes grow, normality appears

[Verse 3]
Asset price movements dance the normal way
Risk models and valuations trust its sway
Mean and variance parameters control the shape
Standard deviation helps no data point escape
Continuous and smooth, infinity's embrace
Normal distribution sets the modeling pace

[Chorus]
Uniform, binomial, normal curves we trace
Each distribution finds its financial place
Flat or binary, bell-shaped destiny
Master these three patterns, unlock what markets see
Distribution nation, probability's foundation

[Outro]
Three distributions rule the analyst's domain
Uniform, binomial, normal – remember the refrain
When data needs a model, know which tool applies
Statistical foundations never tell you lies

← Bayes' Theorem and Total Probability | The Normal Distribution and Beyond →