Read the Shape - distributions and CLT practice
← StatisticsFirst sample of the session.
About Read the Shape
Something is generating numbers and you see them as a histogram. Your job is to name the distribution behind them from six candidates: normal, uniform, exponential, lognormal, binomial and Poisson.
How to tell the six apart
A symmetric bell with no hard edges is normal. Flat with hard edges at both ends is uniform. High at zero and decaying is exponential. Positive with a long right tail is lognormal. Skew is the fastest check: near zero means symmetric, above one means a long right tail.
Two of the six are counts. Binomial is bounded, since you cannot get more than n successes out of n trials. Poisson is unbounded above and has one clear signature: its mean equals its variance.
Why quant interviews test this
Naming the distribution is only half of each round. Once you have it, you are shown the parameters and asked for the mean or the variance, because interviewers want E[X] and Var(X) on demand. The last round averages draws from the most lopsided distribution in the set, and the averages turn into a bell anyway. That is the central limit theorem, the idea quant statistics interviews test most.
More from the Statistics Lab: Twenty Backtests on selection bias and Crack the Bot on regression.