Minimum of Random Variables Interview Questions
Minimum of random variables interview prep for survival probabilities, first arrivals, smallest draws, and common minimum-versus-maximum mistakes.
Candidates preparing for first-arrival, smallest-draw, and order-statistic probability prompts.
Use survival probabilities
For a minimum, it is often easier to ask for the probability that every variable is above a threshold. That tells you whether the minimum has not arrived yet.
First-arrival framing
A minimum often represents the first time something happens: first success, first arrival, first failure, or earliest completion among several processes.
Concrete example
For two fair dice, P(min >= 4) equals P(both dice are at least 4), which is (3/6)^2. Tail probabilities can then be used to reason about the minimum.
Contrast with maximum
Maximum questions often use P(max <= k). Minimum questions often use P(min >= k). The inequality direction is the main setup difference.
Independence check
Products of probabilities require independence. If the variables are dependent, define the joint event directly instead of multiplying marginal probabilities.
Common mistakes
Candidates often copy the maximum setup and flip only the label. Write the event in words to avoid reversing the inequality.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.