In this article, we’ll dive into 5 real data scientist interview questions from industry leaders, provide detailed answers, and explain the key concepts involved. If you’re prepping for a data science interview, this in-depth guide will help you sharpen your understanding and stand out from the competition.

5 Data Scientist Interview Questions from Top Tech Companies (Spotify, Lyft, and More)

1. How do you test whether a new credit risk scoring model works? What data would you look at? (Data Scientist at Block)

Credit risk scoring models are fundamental to fintech companies like Block (formerly Square), banks, and other financial institutions. These models predict the likelihood that a customer will default on a loan or credit obligation. When launching a new model, it’s crucial to rigorously evaluate its performance before deployment.

Step 1: Define the Problem and Metrics

First, clarify the objective: Does the new model predict credit risk better than the existing model? The key metrics to evaluate include:

• Accuracy: The percentage of correct predictions.
• Precision/Recall/F1 Score: Especially important if default cases are rare (imbalanced classes). Read more in this article on sensitivity vs precision.
• AUC-ROC (Area Under the Receiver Operating Characteristic Curve): Measures the model’s ability to distinguish between default and non-default cases.
• KS Statistic (Kolmogorov–Smirnov): Measures the separation between the distributions of predicted probabilities for defaulters and non-defaulters.
• Confusion Matrix: Breaks down true positives, false positives, true negatives, and false negatives.

Step 2: Gather the Right Data

To evaluate the model, you need:

• Historical customer data: Features used for prediction (e.g., age, income, credit history).
• Actual default outcomes: Whether the customer defaulted or not (ground truth labels).
• Existing model predictions: For comparison.
• Segmentation data: To analyze performance across different groups (e.g., age, location, loan types).

Step 3: Design the Testing Approach

• A/B Testing (Champion-Challenger): Randomly assign customers to the old (champion) and new (challenger) models, compare outcomes in real-time or retrospectively. 
• Backtesting/Holdout Validation: Split historical data into training and test sets. Train the model on the training set and evaluate on the test set.
• K-Fold Cross-Validation: For small datasets, rotate the test/train split to maximize use of data.

Step 4: Analyze Results

Suppose we have the following metrics from the old and new models:

The new model outperforms the old on all metrics. But you must also check for:

• Overfitting: Is performance consistent on unseen/holdout data?
• Bias/Fairness: Is the model fair across demographic groups? (e.g., does it disadvantage a certain age or ethnic group?)
• Business Impact: Does the improved prediction translate into better business outcomes (lower default rates, higher approval rates, increased profit)?

Step 5: Monitor After Deployment

Once deployed, monitor the new model’s performance in production. Use statistical process control techniques to detect data drift, concept drift, and other post-deployment issues.

Code Example: Plotting ROC Curve in Python

from sklearn.metrics import roc_curve, auc
import matplotlib.pyplot as plt

fpr, tpr, thresholds = roc_curve(y_true, y_scores)
roc_auc = auc(fpr, tpr)

plt.plot(fpr, tpr, label='ROC curve (area = %0.2f)' % roc_auc)
plt.plot([0, 1], [0, 1], 'k--')
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver Operating Characteristic')
plt.legend(loc="lower right")
plt.show()

2. Given n samples from a uniform distribution [0, d], how to estimate d? (Data Scientist at Spotify)

This question tests your statistical estimation skills, specifically maximum likelihood estimation (MLE) for a uniform distribution. Suppose you have n independent samples \( x_1, x_2, ..., x_n \) from a uniform distribution \( U(0, d) \). How do you estimate the parameter \( d \)?

Step 1: Understanding the Uniform Distribution

If \( X \sim U(0, d) \), the probability density function (PDF) is:

\( f(x) = \frac{1}{d} \), for \( 0 \leq x \leq d \)

Step 2: Maximum Likelihood Estimation (MLE)

The likelihood of observing all samples is:

\( L(d) = \prod_{i=1}^{n} f(x_i) = \left( \frac{1}{d} \right)^n \),
if \( 0 \leq x_i \leq d \) for all \( i \), else 0.

To maximize the likelihood, \( d \) must be at least as large as the largest observed sample, i.e., \( d \geq \max(x_i) \). But increasing \( d \) decreases \( L(d) \), so the optimal (MLE) estimate is:

\( \boxed{d_{MLE} = \max(x_1, x_2, ..., x_n)} \)

Step 3: Unbiased Estimator

The MLE is biased. The expected value of the sample maximum is:

\( E[\max(X_1, ..., X_n)] = \frac{n}{n+1}d \)

Thus, an unbiased estimator for \( d \) is:

\( \boxed{d_{unbiased} = \left(1 + \frac{1}{n}\right) \max(x_1, x_2, ..., x_n)} \)

Summary Table

Python Example

import numpy as np

samples = np.random.uniform(0, 10, size=5)
d_mle = np.max(samples)
d_unbiased = (len(samples) + 1) / len(samples) * d_mle

print("Samples:", samples)
print("MLE estimate for d:", d_mle)
print("Unbiased estimate for d:", d_unbiased)

3. Given that one coupon was used, what is the likelihood that another person will use the coupon - i.e., that both of them will use the coupon? (Data Scientist at Lyft)

Step 1 – Understand the problem
This is a conditional probability:
Let event A = person 1 uses coupon, B = person 2 uses coupon.
We know at least one used it - but the wording “Given that one coupon was used” could mean exactly one was used, or at least one was used.

Often these problems assume \(P(A)=P(B)=p\) with independence, and “one coupon was used” means “at least one used” if not otherwise specified.

Step 2 – Set up with independence and equal probability
Assume P(A)=P(B)=p, A and B independent.
We want P(AB∣A∪B) = P(AB∣A∪B):

\(P(AB∣A∪B)=P(AB)/P(A∪B)=p^2/(p+p−p^2)= p/(2−p)​.\)

Step 3 – But maybe “one coupon was used” means exactly one?
If “one coupon was used” means exactly one (so A∪BA∪B but not both),
then given exactly one used, P(both∣exactly one)=0P(both∣exactly one)=0.

That would be trivial, so probably they meant “at least one.”

Key Concepts Involved

• Conditional Probability
• Complement Rule
• Independence Assumption (unless otherwise specified)

4. Throw a fair coin100 times, what is the probability that you will get more than 75 tails? (Research Scientist at Amazon)

The problem intends to ask about flipping a fair coin 100 times and getting more than 75 tails. Let’s proceed:

Step 1: Model as Binomial Distribution

Let \( X \) = number of tails in 100 tosses.
\( X \sim \text{Binomial}(n=100, p=0.5) \)

Step 2: Calculate Probability Using Normal Approximation

We want \( P(X > 75) = P(X \geq 76) \).

For large \( n \), binomial can be approximated by a normal distribution:

\( \mu = np = 100 \times 0.5 = 50 \)
\( \sigma^2 = np(1-p) = 100 \times 0.5 \times 0.5 = 25 \)
\( \sigma = 5 \)

Apply continuity correction: \( P(X \geq 76) \approx P(Y > 75.5) \), where \( Y \sim N(50, 25) \).

Step 3: Z-Score Calculation

\( Z = \frac{75..5 - 50}{5} = \frac{25.5}{5} = 5.1 \)

Using the standard normal distribution table, the probability that \( Z > 5.1 \) is extremely small:

\( P(Z > 5.1) \approx 1 - 0.99999998 = 0.00000002 \)

In other words, the probability of getting more than 75 tails in 100 fair coin tosses is practically zero.

Step 4: Exact Binomial Calculation (Optional)

For completeness, let’s compute the exact probability using the binomial formula:

\( P(X \geq 76) = \sum_{k=76}^{100} \binom{100}{k} \left(0.5\right)^{100} \)

This sum is dominated by extremely small numbers, so the result remains negligible. Let's demonstrate this with Python:

from scipy.stats import binom

# Probability of getting more than 75 tails in 100 tosses
prob = binom.sf(75, 100, 0.5)  # sf = 1 - cdf(75)
print('Probability:', prob)

Interpretation

This result demonstrates the power of the law of large numbers and the central limit theorem: for large numbers of fair coin tosses, extreme outcomes (like more than 75 tails) are exceedingly unlikely.

Key Concepts Involved

• Binomial Distribution
• Normal Approximation (Central Limit Theorem)
• Z-Score and Standard Normal Table
• Continuity Correction

5. You randomly draw a coin from 100 coins - 1 unfair coin (head-head), 99 fair coins (head-tail) and roll it 10 times. If the result is 10 heads, what's the probability that the coin is unfair? (Data Scientist at Meta)

This is a classic Bayesian probability question that tests your ability to apply Bayes’ theorem in real-world scenarios. Let’s break it down step by step.

Step 1: Define the Problem

• You have 100 coins: 1 double-heads coin (always shows heads), and 99 fair coins.
• You randomly pick one coin and flip it 10 times. You observe 10 heads.
• What’s the probability you picked the unfair (double-heads) coin, given this result?

Step 2: Apply Bayes’ Theorem

Let:

• \( U \): event that you picked the unfair coin
• \( F \): event that you picked a fair coin
• \( H \): event of observing 10 heads in 10 tosses

We want to find \( P(U \mid H) \).

Bayes’ theorem:

\( P(U \mid H) = \frac{P(H \mid U) \cdot P(U)}{P(H \mid U) \cdot P(U) + P(H \mid F) \cdot P(F)} \)

Step 3: Calculate Each Term

• \( P(U) = \frac{1}{100} \) (probability of picking the unfair coin)
• \( P(F) = \frac{99}{100} \)
• \( P(H \mid U) = 1 \) (the unfair coin always shows heads)
• \( P(H \mid F) = (0.5)^{10} = \frac{1}{1024} \) (probability of 10 heads in a row with a fair coin)

Step 4: Plug Values into Bayes’ Formula

\( P(U \mid H) = \frac{1 \cdot \frac{1}{100}}{1 \cdot \frac{1}{100} + \frac{1}{1024} \cdot \frac{99}{100}} \)

\( = \frac{\frac{1}{100}}{\frac{1}{100} + \frac{99}{102400}} \)

\( = \frac{\frac{1}{100}}{\frac{1}{100} + \frac{99}{102400}} \)

To get a common denominator:

\( = \frac{1024}{1024 + 99} = \frac{1024}{1123} \approx 0.912 \)

Step 5: Final Probability

So, the probability that the coin is unfair, given you observed 10 heads, is approximately \( 91.2\% \).

Python Calculation

def prob_unfair_given_heads(n_fair=99, n_unfair=1, flips=10):
    p_unfair = n_unfair / (n_fair + n_unfair)
    p_fair = n_fair / (n_fair + n_unfair)
    p_heads_given_unfair = 1
    p_heads_given_fair = 0.5 ** flips
    numerator = p_heads_given_unfair * p_unfair
    denominator = numerator + p_heads_given_fair * p_fair
    return numerator / denominator

print(prob_unfair_given_heads())  # Output: ~0.912

Key Concepts Involved

• Bayesian Inference
• Conditional Probability
• Likelihood Calculation
• Law of Total Probability

Conclusion: Mastering Data Scientist Interviews at Top Tech Companies

Interviewing for a data scientist role at industry leaders like Spotify, Lyft, Block, Amazon, and Meta means facing questions that probe your understanding of probability, statistics, experimentation, and Bayesian reasoning. These five questions represent common themes:

• Model Evaluation & Experimentation (Block)
• Statistical Estimation (Spotify)
• Conditional Probability (Lyft)
• Central Limit Theorem & Rare Events (Amazon)
• Bayesian Reasoning (Meta)

To ace these interviews:

• Practice explaining your reasoning clearly, step by step.
• Brush up on probability, statistics, and machine learning fundamentals.
• Write code to simulate and verify your answers when possible.
• Discuss the business context and implications of your solutions.

By mastering the concepts and approaches in these real-world interview problems, you’ll be well-prepared to impress your interviewers and land your dream data scientist job at any top tech company.

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