How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Technical Screen rounds at LinkedIn.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at LinkedIn during technical interviews.

Compare queueing systems and common distributions

Quick Overview

LinkedIn data scientist technical-screen statistics question. It evaluates queueing-theory pooling (one shared queue vs. separate queues, compared on expected wait, variance, and fairness), normal vs. mixture distributions for U.S. heights, the right-skewed heavy-tailed distribution of social-network connections with the mode < median < mean ordering, and why L1 (lasso) and L2 (ridge) estimators are biased via the bias–variance tradeoff.

Question

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

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.
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.
Pooled distribution. If you pool men and women together and ignore sex, what does the combined height distribution look like?
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?
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?
Regularization bias. Are the L1-regularized (lasso) and L2-regularized (ridge) estimators unbiased? Why or why not?

Quick Overview

Question

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

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.
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.
Pooled distribution. If you pool men and women together and ignore sex, what does the combined height distribution look like?
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?
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?
Regularization bias. Are the L1-regularized (lasso) and L2-regularized (ridge) estimators unbiased? Why or why not?

Compare queueing systems and common distributions

Quick Overview

Question

Solution

Submit Your Answer to Earn 20XP

Compare queueing systems and common distributions

Quick Overview

Question

Solution

Submit Your Answer to Earn 20XP