An urn has 15 balls in it, including 3 green balls, 5 yellow balls and 7...

 

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An urn has 15 balls in it, including 3 green balls, 5 yellow balls and 7 red balls. Your statistics professor gives you the opportunity to draw two balls in succession (without replacement) in the hopes of getting some extra credit towards your first exam. The downside is that if you attempt the experiment and do not draw one of the "extra credit" events given below, you will lose 5 points on your first exam: A. Draw two green balls: 10 points extra credit B. Draw two yellow balls: 5 points extra credit C. Exactly one of the two balls drawn is green: 3 points extra credit D. One ball is yellow and the other is red: 2 points extra credit X P(X = x) 1. What are the lines of code you used in R to define your discrete probability distribution vectors (remember to check that your probabilities add to exactly one - you will want to work with fractions in R - do not use decimal approximations)? 2. What is the expected extra credit (in points) on the first exam for those who attempt the experiment (rounded to three decimal places)? 3. What is the variance of your discrete probability distribution (rounded to two decimal places)? 4. What is the standard deviation of your discrete probability distribution (rounded to two decimal places)? 5. If all 256 students from both the online and the in person STA 381 classes decide to play the game, how many total extra credit points would you expect to be rewarded (rounded to the nearest integer)? An urn has 15 balls in it, including 3 green balls, 5 yellow balls and 7 red balls. Your statistics professor gives you the opportunity to draw two balls in succession (without replacement) in the hopes of getting some extra credit towards your first exam. The downside is that if you attempt the experiment and do not draw one of the "extra credit" events given below, you will lose 5 points on your first exam: A. Draw two green balls: 10 points extra credit B. Draw two yellow balls: 5 points extra credit C. Exactly one of the two balls drawn is green: 3 points extra credit D. One ball is yellow and the other is red: 2 points extra credit X P(X = x) 1. What are the lines of code you used in R to define your discrete probability distribution vectors (remember to check that your probabilities add to exactly one - you will want to work with fractions in R - do not use decimal approximations)? 2. What is the expected extra credit (in points) on the first exam for those who attempt the experiment (rounded to three decimal places)? 3. What is the variance of your discrete probability distribution (rounded to two decimal places)? 4. What is the standard deviation of your discrete probability distribution (rounded to two decimal places)? 5. If all 256 students from both the online and the in person STA 381 classes decide to play the game, how many total extra credit points would you expect to be rewarded (rounded to the nearest integer)?

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To define the discrete probab... View the full answer