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evolution of the game depends critically on the outcome of the first roll

1,)  Craps is an interesting casino game because it is an example of a random experiment that takes place in stages; the evolution of the game depends critically on the outcome of the first roll. In particular, the number of rolls is a random variable.

The player (known as the shooter) rolls a pair of fair dice

a. If the sum is 7 or 11 on the first throw, the shooter wins; this event is called a natural.

b. If the sum is 2, 3, or 12 on the first throw, the shooter loses; this event is called craps.

c. If the sum is 4, 5, 6, 8, 9, or 10 on the first throw, this number becomes the shooter’s point. The shooter continues rolling the dice until either she rolls the point again (in which case she wins) or rolls a 7 (in which case she loses).

The sum of the scores  on a given roll has the probability density function in the table. The table of bets (not relevant to this problem) is shown in the image.

Setup an experiment to simulate the sum of a single roll of two 6-sided dice.

Run 1000 replications of the experiment.

Analyze the percentage of time the shooter (1) wins on the first roll or (2) loses on the first roll. (Note: we are ignoring item C above for this problem).

Summarize the sample of the SUMS in a frequency distribution, probability distribution, cumulative probability distribution.

Graph the results. 

What would the theorectical probability of winning or losing on the first roll based on classical assignment of probabilities? Graph?

2.) Roulette is the oldest casino game still in operation. It’s invention has been variously attributed to Blaise Pascal, the Italian mathematician Don Pasquale, and several others. In any event, the roulette wheel was first introduced into Paris in 1765. Here are the characteristics of the wheel:

The (American) roulette wheel has 38 slots numbered 00, 0, and 1–36.

Green slot numbers 0, 00;

Red slot numbers 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36;

Black slot numbers 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35

The wheel is spun and then a small ball is rolled in a groove, in the opposite direction as the motion of the wheel. Eventually the ball falls into one of the slots. 

All 38 possible values for a single spin of the wheel are given in the table. Naturally, we assume mathematically that the wheel is fair, so that the random variable X that gives the slot number of the ball is uniformly distributed over the sample space. An image of the roulette wheel and it’s betting table (not relevant to this problem) is shown in the image.

Setup an experiment to simulate the outcome for a single spin of the wheel.

Run 1000 replications of the experiment.

Analyze the percentage of time the a player wins

1) who only bets on the same number for every spin of the wheel

2) who randomly selects a different number every spin

Describe your findings in the management statement

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Writers Solution

Effective financial reporting depends on sound ethical behavior.

Effective financial reporting depends on sound ethical behavior. Financial scandals in accounting and the businesses world have resulted in legislation to ensure adequate disclosures and honesty and integrity in financial reporting. A sound economy is contingent on truthful and reliable financial reporting.

Instructions:

  • Read the following scenario.
  • Answer the questions that follow. This will be a 2-3 page submission in a question and answer format (also in paragraph form). An introduction and conclusion is not required.
  • Refer back to your textbook for guidance on how to think through the scenario.

You have been recently hired as an assistant controller for XYZ Industries, a large, publically held manufacturing company. Your immediate supervisor is the controller who also reports directly to the VP of Finance. The controller has assigned you the task of preparing the year-end adjusting entries.  In the receivables area, you have prepared an aging accounts receivable and have applied historical percentages to the balances of each of the age categories.  The analysis indicates that an appropriate estimated balance for the allowance for uncollectible accounts is $180,000.  The existing balance in the allowance account prior to any adjusting entry is a $20,000 credit balance.

After showing your analysis to the controller, he tells you to change the aging category of a large account from over 120 days to current status and to prepare a new invoice to the customer with a revised date that agrees with the new category.  This will change the required allowance for uncollectible accounts from $180,000 to $135,000. Tactfully, you ask the controller for an explanation for the change and he tells you “We need the extra income, the bottom line is too low.”

Required:

In a 2-3 page paper, discuss the following:

  1. Consider what you have learned relative to ethics and financial reporting. What is the rationale for the calculations/process used to estimate the $180,000 uncollectible allowance?
  2. How do you think the misstatement of funds will impact the income statement and balance sheet?
  3. What is the ethical dilemma you face? What are the ethical considerations? Consider your options and responsibilities as assistant controller.
  4. Identify the key internal and external stakeholders. What are the negative impacts that can happen if you do not follow the instructions of your supervisor?
  5. What are the potential consequences if you do comply with your supervisor’s instructions? Who will be negatively impacted?

Additional Requirements:

  • Use at least one (1) quality academic resource (in addition to your textbook) for this assignment. Note: Wikipedia and similar websites do not qualify as academic resources. You have access to Strayer University’s Online Library at https://research.strayer.edu and the iCampus University Library Research page at https://icampus.strayer.edu/library/research.

Your assignment must follow these formatting requirements:

  • Your paper should be double spaced (Arial or Times Roman 12 pt font) and follow general Strayer Writing Standards (SWS) as they relate to references and citations. Please take a moment to review the SWS documentation for details (more information and an example is included in the Strayer Writing Standards menu link located in your Blackboard).
  • Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.