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How would you answer this using R code ## Problem 1 (Verzani problem 6.2) Roll a pair of dice. Let $X$ be the largest value shown on the two dice. Use `sample()` to simulate five values of $X$. ```{r, echo=FALSE} # This code block resets the random seed in order to get consistent results. This will be hidden in the final document, but YOU MUST NOT CHANGE THIS! set.seed(5292016)

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1. We need to simulate rolling a pair of dice. We can do this by using the sample() function. We will use the argument replace = TRUE to indicate that we are sampling with replacement.

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You roll a fair six-sided die 100 times. Let X be the random variable that is the number of these rolls that show 1, 2. or 3 You then roll the die another 100 times Let Y be the random variable that is the number of these rolls that show Or 2 With simple calculations in R, using the dbinom and pbinom functions, find the following: P(X < 60). P(Y > 60) . P(X =Y)_ P(X >Y)_ Hand in your R commands (which should consist of one line for each question) ad their numerical outputs:

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