Consider the following information and answer the questions. Show all your work. You are a fan...

 

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Consider the following information and answer the questions. Show all your work. You are a fan of the English soccer team NU. It is the end of the season, and there is only one more match to play. Teams are ranked according to the number of points they accumulated throughout the season, where a victory gives three points to the winning side, a tie gives one point to each team, and a defeat gives zero points to the loser. If two or more teams have the same number of points, then they are ranked according to their goal difference (the goal difference is the difference between goals scored and goals received). As of now, the NU has 23 points and a goal difference of -27. This puts them in 17th place of the league, just above relegation. There are 20 teams in the league, and the two at the bottom of the ranking are relegated at the end of the season. Right now, the standings are as follows for the bottom four teams: Position Team Points Goal Difference NU 23 SU 22 TO BW Answer the following 17 18 19 20 The last two games of the season are to be played between these four teams. Specifically, NU is going to play against TC and SU against BW. The matches are going to occur simultaneously so that the results do not influence each other (thus, they are independent events). You know for a fact that if a victory in any of the two games occurs, it will be by one goal of difference. Consider the following random variable X and Y -{ X = 22 22 Y = 527 -28 -29 -30 if NU is not relegated if NU is relegated [1 if BW is not relegated o if BW is relegated 1. Construct the probability distributions of X and Y 2. What is the unconditional probability of NU being relegated? 12 1. What is the probability of BW and NU not being relegated? (2) 3. What is the probability that NU is not relegated conditional on NU losing its match against TC? 5. Which team is more likely to be relegated NU or BW? (the team with the smallest expected value in their probability distribution is the one most likely to be relegated) Consider the following information and answer the questions. Show all your work. You are a fan of the English soccer team NU. It is the end of the season, and there is only one more match to play. Teams are ranked according to the number of points they accumulated throughout the season, where a victory gives three points to the winning side, a tie gives one point to each team, and a defeat gives zero points to the loser. If two or more teams have the same number of points, then they are ranked according to their goal difference (the goal difference is the difference between goals scored and goals received). As of now, the NU has 23 points and a goal difference of -27. This puts them in 17th place of the league, just above relegation. There are 20 teams in the league, and the two at the bottom of the ranking are relegated at the end of the season. Right now, the standings are as follows for the bottom four teams: Position Team Points Goal Difference NU 23 SU 22 TO BW Answer the following 17 18 19 20 The last two games of the season are to be played between these four teams. Specifically, NU is going to play against TC and SU against BW. The matches are going to occur simultaneously so that the results do not influence each other (thus, they are independent events). You know for a fact that if a victory in any of the two games occurs, it will be by one goal of difference. Consider the following random variable X and Y -{ X = 22 22 Y = 527 -28 -29 -30 if NU is not relegated if NU is relegated [1 if BW is not relegated o if BW is relegated 1. Construct the probability distributions of X and Y 2. What is the unconditional probability of NU being relegated? 12 1. What is the probability of BW and NU not being relegated? (2) 3. What is the probability that NU is not relegated conditional on NU losing its match against TC? 5. Which team is more likely to be relegated NU or BW? (the team with the smallest expected value in their probability distribution is the one most likely to be relegated)

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SOLUTION 5121 The load W travels across the beam Determine the ... View the full answer