Research Interview

Practice problems for Research Interview

• Angle Between Clock Hands at 12:15
• Compound Interest Calculation
• Computing the Nth Fibonacci Number Efficiently
• Expected Flips to Get Two Heads
• Multicollinearity Effects in Regression
• Probability of Odd Number of Heads in Fair Coin Tosses
• 12-Ball Weighing Problem
• Bayesian Inference with Unreliable Witnesses
• Coupon Collector Problem: Expected Die Rolls to See All Faces
• Distribution of Sum of Two Uniform Random Variables
• Drawing Balls Until One Color Exhausted
• Effect of Duplicating Data in Linear Regression
• Expected Samples Until Sum Exceeds One
• Linear Interpolation on 2D Points
• Normal Approximation for Binomial: At Least 50 of 400 Pass
• Probability of Meeting at Train Station
• R-Squared Symmetry: Regressing Y on X vs X on Y
• Rolling Mean and Variance in O(1) Time
• Sum of Consecutive Integers
• Two Burning Strings: Measuring 45 Minutes
• Valid Range of Common Correlation for Three Random Variables
• Expected Rolls for Two Consecutive Sixes
• Frog Cover Time on 4 Circular Lily Pads
• Maximum R² from Combined Predictors
• Ten Prisoners Hat Puzzle - Parity Strategy
• Two Egg Problem: Minimum Worst-Case Drops
• Variance of X-Coordinate for Uniform Points on Unit Circle