Picking the wrong distribution silently breaks your model: counts are not Gaussian, and treating them that way predicts negative events and underestimates the variance of busy periods. The decision tree by data type, the variance gotcha, and what each choice implies for the model you reach for.
Updated Aug 2026 · Grounded in real Forward Deployed Engineer interview loops and written to a senior-engineer editorial bar.
Picking the wrong distribution silently breaks your model: counts are not Gaussian, and treating them that way predicts negative events and underestimates the variance of busy periods. The decision tree by data type, the variance gotcha, and what each choice implies for the model you reach for.
The screen is whether the candidate selects a distribution from the nature of the quantity (binary, count, continuous) and knows the practical tells, especially the Poisson variance-equals-mean property and overdispersion, rather than defaulting to Normal for everything. The reserved follow-up is 'your count data has variance much larger than its mean, what now': the answer is overdispersion, switch to negative binomial, and naming it unprompted is the signal.
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