Deca-Die II

Order statistics and the expected value of a maximum

This is a hard probability question that tests your ability to reason about order statistics—specifically, the distribution of the maximum across independent random variables. Questions like this appear in quant interviews to assess whether you can move beyond simple expectation calculations and handle the machinery of extreme-value theory.

To solve it, you need to derive the cumulative distribution function (CDF) of the maximum, then compute its expectation. The key insight is that the maximum takes a value at most k if and only if all ten dice show values at most k. From there, you can build the probability mass function and sum to find . Precision matters: the answer is expected to two decimal places, so your arithmetic and formula must be exact.

• CDF and PMF of order statistics
• Independence and joint distributions
• Direct summation vs. tail-sum formulas for expectation