Use the above command to simulate rolls of a die when you implement a MATLAB function of the form function Strategy(minFirstRoll,minSecRoll)

Here is a simple game: a player can roll a fair, six-sided die up to three times. After each roll a playermay stop the game and receive $1 for each dot on the upturned die. The player has to roll at least once, andthe game automatically stops after the third roll.

For example, if a player rolls 1, rolls 4, and then stops,the player receives $4. The purpose of this exercise is to determine a good strategy to play this game, onethat maximizes the chances of winning the most money. a. The MATLAB command rand yields a uniformly distributed, random number between 0 and 1. Thereforethe statementceil(6*rand)provides a 1, 2, 3, 4, 5 or 6 each with probability 1/6. We may thus interpret the result of the above MATLABstatement to be the occurrence of a roll of a fair, six-sided die.

Use the above command to simulate rolls of a die when you implement a MATLAB function of the form function Strategy(minFirstRoll,minSecRoll).Strategy(minFirstRoll,minSecRoll) simulates the outcome of the strategy that stops if the outcome ofthe first roll is at least minFirstRoll and stops if the outcome of the second roll at least minSecRoll. TheStrategy function inputs two integers between 1 and 6 and outputs the number representing the upturneddie where the player employing the strategy in question stops. Note: the output of Strategy is a random number.

b. We seek to find which strategies do well on average, so we need to average the results in part a.Write a functionAveStrategy(minFirstRoll,minSecRoll,numGames)that computes the arithmetic average of Strategy(minFirstRoll,minSecRoll) after playing numGamesgames. command line outputs of AveStrategy(1,2,10000), AveStrategy(4,3,10000)and AveStrategy(5,5,10000).

c. Of the strategies considered above, which one does best? and what is its average (as the number ofgames played gets larger and larger)? Remarks: For parts a and b, provide the MATLAB code you wrote for the Strategy and AveStrategyfunctions; for part b, also provide your numerical results; for part c, just answer the questions

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