Question: A fair 20-sided die is rolled repeatedly, until a gambler decides to stop. The gambler receives the amount shown on the die when the gambler stops. The gambler decides in advance to roll the die until a value of m or greater is obtained, and then stop (where m is a fixed integer with 1 ≤ m ≤ 20).
(a) What is the expected number of rolls (simplify)?
(b) What is the expected square root of the number of rolls (as a sum)?