Assignment 2: Probability Analysis

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TipsforM4A2.pptx

Explanation

A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed the choices to two: large facility or small facility. The company has collected information on the payoffs. It now has to decide which option is the best using probability analysis, the decision tree model, and expected monetary value.

Complete the decision tree

Complete the calculations

Explain the decision

Use the numbers and outline from the assignment directions

Use the Statistical Handout in the directions; look for the directions for the terms in red.

Prepare before you panic

Look at this short video on Decision Tree Analysis:

https://www.youtube.com/watch?v=ydvnVw80I_8

https://www.youtube.com/watch?v=a5yWr1hr6QY

EMV and Decision Trees:

https://www.youtube.com/watch?v=fuBLLLPmUqg

Draw a decision tree based on the information in the assignment directions. Also, look for the directions on expected values.

How to get started with Decision Tree Analysis

As a starting point for the decision tree, draw a small square around the center of the left side of the paper. If the description is too large to fit the square, use legends by including a number in the tree and referencing the number to the description either at the bottom of the page or in another page.

Draw out lines (forks) to the right of the square box. Draw one line each for each possible solution to the issue, and describe the solution along the line. Keep the lines as far apart as possible to expand the tree later.

Illustrate the results or the outcomes of the solution at the end of each line. If the outcome is uncertain, draw a circle (chance node). If the outcome leads to another issue, draw a square (decision node). If the issue is resolved with the solution, draw a triangle (end node). Describe the outcome above the square or circle, or use legends, as appropriate.

Repeat steps 2 through 4 for each new square at the end of the solution lines, and so on until there are no more squares, and all lines have either a circle or blank ending.

The circles that represent uncertainty remain as they are. A good practice is to assign a probability value, or the chance of such an outcome happening.

Complete This Decsion Tree; Complete the Calculations

Determination of chance probability and respective payoffs:

Build Small:
Low Demand 0.4($40)=$16
High Demand 0.6($55)=$33

Determination of Expected Value of each alternative Build Small: $16+$33=$49 Build Large: $20+$42=$62

Prepare before you panic

Look at the step by step directions on chance probability in the Statistical Terms handout

Use Excel if that helps you with the decision tree:

https://www.techwalla.com/articles/how-to-draw-a-decision-tree-in-excel

Determination of chance probability and respective payoffs:

Build Large
Low Demand 0.4($50)=$20
High Demand 0.6($70)=$42

Determination of Expected Value of each alternative Build Small: $16+$33=$49 Build Large: $20+$42=$62

EMV

Calculate the Expected Monetary Value (EMV) of each alternative action on your decision tree.

 

HOW TO USE IT/CALCULATE IT?

 

1. Determine the optimal decision and its expected return for the possible outcomes of the sample using the posterior probabilities for the states of nature

2. Calculate the values of the optimal returns

3. Subtract the EV of the optimal decision obtained without using the sample information from the amount determined in step (2)