Compute expected max/min of n die rolls
Problem
You are given a fair six-sided die. You roll this die n times, with each roll being independent of the others.
- Compute the expected value of the maximum roll observed across all
nrolls. - Compute the expected value of the minimum roll observed across all
nrolls.
Provide a formula for both expected values, expressed in terms of n.
AI interview prep
Core dilemma
The central challenge is to correctly apply probability theory, specifically order statistics for independent and identically distributed (i.i.d.) discrete random variables, to derive the expected values of the maximum and minimum outcomes. It tests foundational understanding of probability distributions rather than system design.
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Interview prep
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Compute expected max/min of n die rolls
Problem
You are given a fair six-sided die. You roll this die n times, with each roll being independent of the others.
- Compute the expected value of the maximum roll observed across all
nrolls. - Compute the expected value of the minimum roll observed across all
nrolls.
Provide a formula for both expected values, expressed in terms of n.