Suppose you roll a die until the first time you obtain an even number. Let X1​ be the total number of times you roll a 1, and let X2​ be the total number of times that you roll a 2. Use simulation in R to test if E[X1​]=E[X2​]. Include a screenshot of the RStudio approach. Hint: It is extremely unlikely that you will roll 30 times before getting the first even number, so you can safely assume that the first even roll occurs inside of 30 rolls. E[X1​]=E[X2​] or E[X1​]≠E[X2​]

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Suppose you roll a die until the first time you obtain an even number. Let X1​ be the total number of times you roll a 1, and let X2​ be the total number of times that you roll a 2.

Use simulation in R to test if E[X1​]=E[X2​]. Include a screenshot of the RStudio approach.

Hint: It is extremely unlikely that you will roll 30 times before getting the first even number, so you can safely assume that the first even roll occurs inside of 30 rolls.

  • E[X1​]=E[X2​]

or

  • E[X1​]≠E[X2​]
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