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Compare queueing systems and common distributions

LinkedInData Scientist · Technical Screen
MediumData ScientistTechnical ScreenStatistics & Math

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LinkedIn data scientist statistics screen covering pooled versus separate queues, height distributions and mixture distributions, right-skewed network degree, mean-median-mode ordering, and L1/L2 regularization bias.

Question

You are asked a series of statistics fundamentals questions in a data science technical screen.

  1. Queueing. A bank with 5 tellers can be organized two ways:
  • System A: all 5 tellers share one common queue.
  • System B: each teller has their own separate queue.

Assume customer arrivals are random, tellers are similarly (but not necessarily identically) skilled, customers are served first-come-first-served within a line, and some customers take much longer than others. As a customer, which system would you rather join, and why? Compare the two in terms of expected waiting time, variance of waiting time, and fairness.

  1. Height distributions. Sketch or describe the distribution of adult male heights in the United States and, separately, the distribution of adult female heights in the United States.

  2. Pooled distribution. If you pool men and women together and ignore sex, what does the combined height distribution look like?

  3. Network degree. On a social network such as LinkedIn, describe the distribution of the number of connections per user. Is it symmetric, left-skewed, or right-skewed?

  4. Summary statistics. For that connections distribution, how do the mean, median, and mode compare, and why? If asked for the likely scale of the mean, what factors would determine it?

  5. Regularization bias. Are the L1-regularized (lasso) and L2-regularized (ridge) estimators unbiased? Why or why not?