Mathematics, 24.10.2019 23:43 grettelyesenia
In a casino game, gamblers are allowed to roll n fair, 6-sided dice. if a 6 shows up on any of them, the gambler gets nothing. if no 6’s appear, the gambler is paid the sum of the values on the dice in dollars. the gambler is free to choose n, the number of dice rolls.
a) derive a formula for the gambler’s expected payoff (the total dollars won). plot this payoff for values of n from 1 to 20. what is the smallest n that maximizes the expected payoff ?
b) suppose the gambler chooses to roll 10 dice (this is not necessarily the answer to part ( what is the expected number of distinct dice values that show up? in other words, what is the expected number of faces that are rolled at least once?
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