The Gardener's Sunflowers

What this expected-value interview question tests

This is a medium-difficulty probability problem that combines sequential decision-making with expectation. It asks you to reason about the expected number of times a running maximum is updated as you process a sequence of random values left to right. Quant firms use problems like this to assess whether you can translate a process into a mathematical framework and compute expectations without simulation.

The key insight is recognizing that each position has a well-defined probability of being "kept" — that is, being taller than all previous plants. Once you identify that probability for each position, summing them gives the expected total by linearity of expectation. The challenge is deriving those probabilities cleanly and handling the arithmetic precisely.

• Linearity of expectation for indicator random variables
• Conditional probability and symmetry arguments
• Order statistics and running extrema