[Verse 1] Picture data scattered like autumn leaves across a field Some numbers low, some numbers high, but patterns get revealed When we collect a thousand points and sketch them on a chart A mountain shape emerges with symmetry at heart [Chorus] Bell curve dancing, sixty-eight between the lines Two standard deviations catch ninety-five designs Normal distribution, our statistical crown Mean and median kissing in the center of town [Verse 2] But markets don't behave like textbook theory says Stock prices jump and crash in unpredictable ways When normal gets transformed by exponential flight We birth the lognormal, skewed heavy to the right [Chorus] Bell curve dancing, sixty-eight between the lines Two standard deviations catch ninety-five designs Student's t-distribution when samples get too small Fatter tails protecting from overconfident calls [Bridge] Chi-square measures variance, testing if we're right F-distribution compares two variances in sight Degrees of freedom matter, they shape each curve's design From skinny peaks to rolling hills, each tells a different rhyme [Verse 3] When sample size grows mighty, t-distribution fades Approaching normal limits as uncertainty degrades But when we're testing portfolios with limited observations These distributions guard us from false correlations [Chorus] Bell curve dancing, sixty-eight between the lines Two standard deviations catch ninety-five designs Normal distribution, our statistical crown Mean and median kissing in the center of town [Outro] From Gaussian foundations to the tails that stretch beyond Each distribution serves us in this mathematical pond
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