Implement Jackknife and Random Choice
Company: Pinterest
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Technical Screen
Write Python code for two implementation tasks without using `np.random.choice` directly:
1. **Jackknife-style resampling.** Given a one-dimensional collection of observations `x` of length `n`, generate all `n` leave-one-out samples. For a supplied statistic function `f(sample)`, compute the statistic on each leave-one-out sample and return the jackknife estimate of bias and variance. Your implementation should work when the input is either a Python list or a pandas DataFrame with one row per observation.
2. **Random choice sampler.** Given an array `values`, a probability vector `p` such that `sum(p) = 1`, and an integer `k`, implement a simplified version of `np.random.choice` that returns `k` samples according to `p`. Discuss how your approach differs for sampling with replacement versus without replacement, and state the expected time complexity.
Quick Answer: This question evaluates understanding of statistical resampling (jackknife), probabilistic sampling algorithms including with- and without-replacement selection, and proficiency with Python data structures and numerical libraries for implementing estimators.