Sample two numbers from 1 to 10; maximize the expected product Assume you sample two numbers, randomly drawn from 1 to 10; you could choose two strategies: 1) pick with replacement and 2) pick without replacement. Which strategy would you prefer to maximize the expected product?
I encountered this problem while preparing for an interview. My intuition is picking with replacement would be better. However, I found it too complex to use the brute-force method to prove it. Could anyone suggest a better approach?

I would pick 10 twice, this results in 100 which is the largest possible product of two numbers between 1 and 10.
