MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question

1. Present the probability distribution for the sum of two six-sided dice (i.e., list the possible values of the random variable, X and each value’s corresponding probability). Use the x-axis above and rules of theoretical probability to help you calculate your probabilities. (Hint: there are 36 outcomes.) Present the probabilities as fractions (simplified or not simplified) or decimals (rounded to four decimal places) in a table.

2. Now calculate the theoretical probability that the player lands on “Reading Railroad” on their first turn. Using the probability distribution built in number 1, state this probability as a decimal rounded to four decimal places in a sentence.

3. Calculate the theoretical probability that the player will move no farther than “Reading Railroad” on the first turn. Using the probability distribution built in number 1, state this probability as a decimal rounded to four decimal places in a sentence.

4. Calculate the theoretical probability that the player moves farther than “Reading Railroad” on their first turn. Using the probability distribution built in number 1 state this probability as a decimal rounded to four decimal places in a sentence.

**Transcription of Simulation Interface and Instructions for Educational Use** **Introduction:** This image demonstrates the interface of a simulation tool used for analyzing the outcomes of rolling two six-sided dice. Here’s a detailed guide to understanding and utilizing the tool effectively for educational purposes. **Interface Overview:** 1. **Top Panel Options:** - **Runs**: Options include performing 1 run, 5 runs, or 1000 runs of dice rolls. - **Controls**: Buttons to Reset, Analyze, and view Info about the simulation. 2. **Event Configuration:** - The interface allows users to set up scenarios for analyzing the sum of two dice rolls. 3. **Box 1 (Inequality Adjustment):** - **Instructions**: Use the down arrow to change the equality/inequality sign. Choices include: >=, >, =, <=, or <. 4. **Box 2 (Value Input):** - **Instructions**: Use this box to enter specific numerical values relevant for parts (b)-(d) of the analysis exercise. 5. **Graph and Results Section:** - **Vertical Axis**: Labeled as "Frequency," indicating how often a specific sum appears. - **Horizontal Axis**: Labeled as "Sum of 2 rolls," showing possible outcomes from 2 to 12. - **Output Box**: The section where calculated results will be displayed. 6. **User Guidance:** - “You only need to adjust the information in Boxes 1 and 2 to answer parts (b)-(d).” 7. **Results Display:** - A designated area marked "YOUR RESULT WILL APPEAR HERE" is where outcomes from adjusted parameters will be shown after running simulations. **Conclusion:** This simulation tool is designed to provide a hands-on experience with probability and combinatorics through the analysis of dice rolls. Follow the instructions to manipulate the parameters and observe the outcomes, enhancing understanding of probability distributions and frequency analysis.
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Transcribed Image Text:**Transcription of Simulation Interface and Instructions for Educational Use** **Introduction:** This image demonstrates the interface of a simulation tool used for analyzing the outcomes of rolling two six-sided dice. Here’s a detailed guide to understanding and utilizing the tool effectively for educational purposes. **Interface Overview:** 1. **Top Panel Options:** - **Runs**: Options include performing 1 run, 5 runs, or 1000 runs of dice rolls. - **Controls**: Buttons to Reset, Analyze, and view Info about the simulation. 2. **Event Configuration:** - The interface allows users to set up scenarios for analyzing the sum of two dice rolls. 3. **Box 1 (Inequality Adjustment):** - **Instructions**: Use the down arrow to change the equality/inequality sign. Choices include: >=, >, =, <=, or <. 4. **Box 2 (Value Input):** - **Instructions**: Use this box to enter specific numerical values relevant for parts (b)-(d) of the analysis exercise. 5. **Graph and Results Section:** - **Vertical Axis**: Labeled as "Frequency," indicating how often a specific sum appears. - **Horizontal Axis**: Labeled as "Sum of 2 rolls," showing possible outcomes from 2 to 12. - **Output Box**: The section where calculated results will be displayed. 6. **User Guidance:** - “You only need to adjust the information in Boxes 1 and 2 to answer parts (b)-(d).” 7. **Results Display:** - A designated area marked "YOUR RESULT WILL APPEAR HERE" is where outcomes from adjusted parameters will be shown after running simulations. **Conclusion:** This simulation tool is designed to provide a hands-on experience with probability and combinatorics through the analysis of dice rolls. Follow the instructions to manipulate the parameters and observe the outcomes, enhancing understanding of probability distributions and frequency analysis.
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