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Questions and Answers
What is the probability of rolling a sum of 10 with two dice?
What is the probability of rolling a sum of 10 with two dice?
What is the probability of event B, P(B)?
What is the probability of event B, P(B)?
If event A is rolling a '1 or 2', what is the probability of the event B, which is rolling '3 or 4 or 5 or 6'?
If event A is rolling a '1 or 2', what is the probability of the event B, which is rolling '3 or 4 or 5 or 6'?
What is the complement of the event of rolling a '2' on a die?
What is the complement of the event of rolling a '2' on a die?
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What is the sum of the probabilities of events A, B, and C if they are mutually exclusive and collectively exhaustive?
What is the sum of the probabilities of events A, B, and C if they are mutually exclusive and collectively exhaustive?
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What does P(A ∩ B) represent in probability theory?
What does P(A ∩ B) represent in probability theory?
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Using the multiplication rule for independent events, what is the probability of rolling 'not 1' on the first die and '2' on the second die?
Using the multiplication rule for independent events, what is the probability of rolling 'not 1' on the first die and '2' on the second die?
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What is the total number of outcomes in the sample space when rolling two dice?
What is the total number of outcomes in the sample space when rolling two dice?
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Which of the following correctly represents the probability of event C, P(C)?
Which of the following correctly represents the probability of event C, P(C)?
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If P(A ∪ C) = 7/10, what can we infer about events A and C?
If P(A ∪ C) = 7/10, what can we infer about events A and C?
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What is the expected duration calculated from the given p-values?
What is the expected duration calculated from the given p-values?
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What is the expected value when rolling a single die?
What is the expected value when rolling a single die?
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What is the expected value when rolling four dice?
What is the expected value when rolling four dice?
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If the probability of getting an odd number is twice that of getting an even number, what is the expected value of rolling a die?
If the probability of getting an odd number is twice that of getting an even number, what is the expected value of rolling a die?
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Which formula represents the calculation of expected value when rolling a single die?
Which formula represents the calculation of expected value when rolling a single die?
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What is one topic covered in Week 04 of the PMGT3623 course?
What is one topic covered in Week 04 of the PMGT3623 course?
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Which assessment has the highest weight in the PMGT3623 course?
Which assessment has the highest weight in the PMGT3623 course?
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Which technique is mentioned as part of the probabilistic approach for project scheduling?
Which technique is mentioned as part of the probabilistic approach for project scheduling?
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In which week is the Knowledge Test scheduled?
In which week is the Knowledge Test scheduled?
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What is the weight of the Group Assignment Presentation in the PMGT3623 assessments?
What is the weight of the Group Assignment Presentation in the PMGT3623 assessments?
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Which of the following weeks focuses on the implementation of the Project Network Diagram using Microsoft Project?
Which of the following weeks focuses on the implementation of the Project Network Diagram using Microsoft Project?
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What is the probability of the Fast Completion scenario in the project?
What is the probability of the Fast Completion scenario in the project?
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What is the purpose of the probabilistic approach to project scheduling?
What is the purpose of the probabilistic approach to project scheduling?
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Which aspect is not a characteristic of the beta distribution?
Which aspect is not a characteristic of the beta distribution?
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Which week involves a mid-semester break in the PMGT3623 schedule?
Which week involves a mid-semester break in the PMGT3623 schedule?
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What happens in the case where the sum of the probabilities for the scenarios does not equal 1?
What happens in the case where the sum of the probabilities for the scenarios does not equal 1?
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What is true about the beta distribution when both parameters α and β are equal?
What is true about the beta distribution when both parameters α and β are equal?
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How does the beta distribution compare to the normal distribution in terms of accuracy for estimation?
How does the beta distribution compare to the normal distribution in terms of accuracy for estimation?
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What is the expected value of Project A?
What is the expected value of Project A?
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Which of the following options has the highest expected value?
Which of the following options has the highest expected value?
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What is the expected value of the Bank Deposit?
What is the expected value of the Bank Deposit?
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In which scenario does the expected value equal the average?
In which scenario does the expected value equal the average?
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What would be the expected value if the probabilities in Project A changed to 80% for success?
What would be the expected value if the probabilities in Project A changed to 80% for success?
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What happens to the expected value if all outcomes have different probabilities?
What happens to the expected value if all outcomes have different probabilities?
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Which calculation method is used to determine expected value in investments?
Which calculation method is used to determine expected value in investments?
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If your company chooses Project B, what is the potential maximum loss?
If your company chooses Project B, what is the potential maximum loss?
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Study Notes
PMGT3623 Scheduling - Week 4
- Topic: Probabilistic Approach to Project Network Diagram - Part I
- Probabilistic Approach: A project management approach needed for complex projects because task durations are often uncertain. Using a deterministic approach is appropriate for simple projects.
- Need for Probabilistic Approach: The previous week's deterministic approach to task duration is suitable for simple projects, but complex projects' uncertain task durations require a probabilistic approach.
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Topics Covered (Week 4, Part 1):
- Why is a probabilistic approach needed in project network diagrams?
- Probability and probability distributions
- Expected Value
- Beta Distribution
- Program Evaluation and Review Technique (PERT)
Probability and Probability Theory
- Probability Definition: The probability of an event is a value between 0 and 1 representing the chance of the event occurring. It's calculated as the number of favorable outcomes divided by the total number of possible outcomes.
- Sums of Probabilities: The sum of probabilities of mutually exclusive and collectively exhaustive events equals 1.
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Sets and Probability:
- A set is a collection of well-defined, distinct objects.
- Subsets: If every member of set A is also a member of set B, then A is a subset of B.
- Set Operations: ∪ (Union), ∩ (Intersection)
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Probability Examples:
- Coin toss
- Dice roll calculation
Probability Distribution: Beta Distribution
- Beta Distribution: A family of continuous probability distributions defined on the interval [0,1] parametrized by two positive shape parameters (α and β). It models variables with a constrained range, useful for projects with limited ranges/outcomes.
- Beta Distribution Usefulness: It's crucial for improved project estimation and more accurate task activity durations. Used to provide more reliable estimates of completion times when compared to approaches like the normal distribution, which don't account for the limited intervals of task durations.
- Beta Distribution Shape: The shape of the beta distribution is determined by the parameters α and β. When α and β are equal, the distribution is symmetric. Increasing the values of α and β reduces the variance.
Beta Distribution and PERT
- PERT (Program Evaluation and Review Technique): A network analysis technique for managing uncertainty in task durations. It is based on beta-distribution principles and used when task durations have high degrees of uncertainty.
- PERT Weighted Average: A formula (O + 4ML + P) / 6, where 'O' is an Optimistic estimate, 'ML' is a Most likely estimate, and 'P' is a Pessimistic estimate. It is used to calculate expected completion time.
- Standard Deviation: The standard deviation of a task estimate is calculated from PERT values, and its formula is (P-O)/6. The formula defines a relationship between project completion time and beta-distribution estimates.
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Expected Value Examples:
- Various task duration estimations
Expected Value
- Expected Value: A calculation technique used to estimate the average outcome of various project stages, based on their probabilities and associated values.
- Expected Value Formula: The sum of the products of each possible outcome by its associated probability ( Σ xᵢ * P(xᵢ) )
- Expected Value Usefulness: Used in decision-making, project planning, and overall project outcomes, based on probability estimates and task durations.
- Expected Value Exercise: Given various project scenarios with different probabilities and durations, estimate the overall project completion time and standard deviation using PERT (Program Evaluation Review Technique).
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Description
Dive into the probabilistic approach necessary for project network diagrams in complex projects. This quiz covers the importance of probability, expected value, Beta distribution, and the Program Evaluation and Review Technique (PERT) used in project management. Prepare to enhance your understanding of these critical concepts.
