Explain core probability and ML statistics concepts
Core Probability and ML Statistics Concepts
This interview assesses your foundational understanding of key concepts in probability, basic statistics, linear regression, and Principal Component Analysis (PCA). You should be prepared to define terms, explain underlying principles, derive formulas, and discuss practical implications.
Probability
- You roll two fair six-sided dice.
- What is the probability that one die shows a strictly larger value than the other (i.e., the two values are different and one is greater)?
- What is the probability that a specific die (e.g., the first die) is strictly larger than the other?
Basic Statistics
- Define mean and variance of a random variable.
- Is the usual sample variance estimator “biased”? If yes, what correction makes it unbiased?
Correlation vs. Independence
- Let X and Y be (marginally) normally distributed with a correlation of zero (Corr(X,Y)=0). Are X and Y necessarily independent? State the condition under which zero correlation does imply independence.
Linear Regression / OLS
- Explain linear regression and list common assumptions behind Ordinary Least Squares (OLS).
- Write the closed-form OLS estimator.
- Why is (multi)collinearity a problem in regression? How can you detect it, and how can you mitigate it?
- Briefly explain Ridge and Lasso regression and how they relate to collinearity.
PCA
- Explain Principal Component Analysis (PCA).
- What are eigenvalues and eigenvectors in this context, and what do they represent?
- List key limitations of PCA.
AI interview prep
Core dilemma
The central engineering conflict is balancing precise theoretical understanding of statistical and ML concepts with the ability to articulate their practical implications, limitations, and appropriate application in real-world data science scenarios.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Explain core probability and ML statistics concepts
Core Probability and ML Statistics Concepts
This interview assesses your foundational understanding of key concepts in probability, basic statistics, linear regression, and Principal Component Analysis (PCA). You should be prepared to define terms, explain underlying principles, derive formulas, and discuss practical implications.
Probability
- You roll two fair six-sided dice.
- What is the probability that one die shows a strictly larger value than the other (i.e., the two values are different and one is greater)?
- What is the probability that a specific die (e.g., the first die) is strictly larger than the other?
Basic Statistics
- Define mean and variance of a random variable.
- Is the usual sample variance estimator “biased”? If yes, what correction makes it unbiased?
Correlation vs. Independence
- Let X and Y be (marginally) normally distributed with a correlation of zero (Corr(X,Y)=0). Are X and Y necessarily independent? State the condition under which zero correlation does imply independence.
Linear Regression / OLS
- Explain linear regression and list common assumptions behind Ordinary Least Squares (OLS).
- Write the closed-form OLS estimator.
- Why is (multi)collinearity a problem in regression? How can you detect it, and how can you mitigate it?
- Briefly explain Ridge and Lasso regression and how they relate to collinearity.
PCA
- Explain Principal Component Analysis (PCA).
- What are eigenvalues and eigenvectors in this context, and what do they represent?
- List key limitations of PCA.