Unformatted text preview: Introduction to Statistics Project #4: Designing a Fair Game of Chance Introduction Your task for this project is to create your own completely original game of chance involving at least two random events (dice, coin flips, cards, spinners, etc.) The game should involve at least three different ways to win and at least three different ways to lose, with each outcome having a mathematically appropriate reward or loss. Objectives: You will be able to construct a probability distribution for a random variable. You will be able to find the mean, variance, and expected value for a discrete random variable You will be able to determine if a game of chance is "fair" Game requirements The game should be based on chance of at least two random events. The game should have at least three ways to win and at least three different ways to lose, each with various probabilities (i.e. Big Win, Medium Win, Small Win, etc.) Each win or loss outcome should have a reward or loss (points or money). The game should be statistically fair. In other words the expected or average value of the reward/loss should be zero. The game should be creative and incorporate something that you're interested in for example you can use a theme like basketball, stock market. Additional Guidelines You can work individually or in teams of two. Scoring Rubric 2 Some information from the name of each student in the group, the date, and the title of the project is indicated on the project Game Rules Very clearly written Written game rules Clearly written game game rules indicate all indicate some of the rules indicate most of of the following: following: the following: Game procedures Game procedures Game procedures Materials needed Materials needed Materials needed How the game is won How the game is won How the game is won or lost. or lost. or lost. Rewards for wins or Rewards for wins or Rewards for wins or penalties for losses penalties for losses penalties for losses Probability A very clearly written A probability A clearly written Distribution probability distribution probability distribution distribution indicates indicates all possible most possible win or indicates all possible win or loss outcomes loss outcomes and their win or loss outcomes and their probabilities probabilities with two and their probabilities with no mistakes. If or three mistakes. If with one or two minor mistakes. If possible, possible, supporting possible, supporting diagrams such as tables supporting diagrams diagrams such as tables such as tables or tree or tree diagrams or tree diagrams diagrams illustrate all illustrate all possible illustrates possible possible outcomes. outcomes. outcomes. Mean or The mean or expected The mean or expected The mean or expected Expected value of the reward/loss value of the reward/loss value of the reward/loss Value is accurately calculated . is accurately calculated. is calculated. Work is Calculation Work is shown with no Work is shown with one shown with two or mistakes. The properly or two minor mistakes. three mistakes. The calculated mean proves The properly calculated game is not a fair game. mean proves that the that the game is game is statistically fair. statistically fair. Variance and The variance and The variance and The variance and Standard standard deviation of standard deviation of standard deviation of Deviation the rewards/losses is the rewards/losses is the rewards/losses is Calculation accurately calculated. calculated. Work is calculated. Work is Work is shown with no shown with one or two shown with two or three mistakes. mistakes. minor mistakes. Creativity, Fun, The game is very The game is creative The game is creative and creative and fun for all and fun for most and fun for some players. Some players Excitement players. Everybody players. Most players want to play more wants to play more want to play more because it's fun and because it's fun and because it's fun and exciting. exciting. exciting. On Time Project is completed on Project is completed Project is completed or before the due date: within one day of due within three days of due Beginning of class date: date: Wednesday, December Beginning of class on Beginning of class on 17 Wednesday, December Wednesday, December 17 17 Element Name Date Title 4 The name of each student in the group, the date, and the title of the project is clearly indicated on the project 3 The name of each student in the group, the date, and the title of the project is indicated on the project 1 No name, date, and title information is included in the project Game rules are not written or lack most of the following: Game procedures Materials needed How the game is won or lost. Rewards for wins or penalties for losses A probability distribution is not included or has many major mistakes. The mean or expected value of the reward/loss is not calculated or the work contains more than three mistakes. The game is not fair. The variance and standard deviation of the rewards/losses is not calculated or contains more than three mistakes. The game is creative and fun for few players. Few players want to play more because it's kind of boring. Project is completed more than three days of due date: Beginning of class on Wednesday, December 17 ...
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- Spring '11
- Statistics, Probability theory, one day, three days