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Questions and Answers
When a variable can take on different values, it is a:
When a variable can take on different values, it is a:
- Random variable (correct)
- Dependent variable
- Exogenous variable
- Independent variable
The expected value is:
The expected value is:
- The product of the sums of the probability and the values in different states
- The sum of the products of the probability and the values in different states (correct)
- The difference between the products of the probability and the values in different states
- The difference between the sums of the probability and the values in different states
Heads and tails are equally likely, but you win a dollar on heads and lose a dollar on tails. The expected value is:
Heads and tails are equally likely, but you win a dollar on heads and lose a dollar on tails. The expected value is:
- $0.50
- $1.00
- $0.00 (correct)
- -$0.50
Heads and tails are equally likely, but you win $2.00 on heads and lose $1.00 on tails. The expected value is:
Heads and tails are equally likely, but you win $2.00 on heads and lose $1.00 on tails. The expected value is:
Heads and tails are equally likely, but you win $3.00 on heads and lose $1.00 on tails. The expected value is:
Heads and tails are equally likely, but you win $3.00 on heads and lose $1.00 on tails. The expected value is:
You can invest $100,000 into either project A or B. You estimate that A succeeds with probability 0.7, doubling in value if it succeeds. Project B succeeds with probability 0.6. You should invest in:
You can invest $100,000 into either project A or B. You estimate that A succeeds with probability 0.7, doubling in value if it succeeds. Project B succeeds with probability 0.6. You should invest in:
You can invest $100,000 into either project A or B. You estimate that A succeeds with probability 0.6, while project B succeeds with probability 0.7. You should invest in:
You can invest $100,000 into either project A or B. You estimate that A succeeds with probability 0.6, while project B succeeds with probability 0.7. You should invest in:
You can invest $100,000 into either project A or B. You estimate that A succeeds with probability 0.5 while project B succeeds with probability 0.8. You should invest in:
You can invest $100,000 into either project A or B. You estimate that A succeeds with probability 0.5 while project B succeeds with probability 0.8. You should invest in:
You can invest in either project A or B. Project A has value $100 with probability 0.1 and value $75 with probability 0.9. Project B has value $110 with probability 0.2 and value $70 with probability 0.8. You should invest in:
You can invest in either project A or B. Project A has value $100 with probability 0.1 and value $75 with probability 0.9. Project B has value $110 with probability 0.2 and value $70 with probability 0.8. You should invest in:
Three possibilities are equally likely with payoffs of $3, $6, and $9. The expected value is:
Three possibilities are equally likely with payoffs of $3, $6, and $9. The expected value is:
Four possibilities are equally likely with payoffs of $2, $4, $6, and $8. The expected value is:
Four possibilities are equally likely with payoffs of $2, $4, $6, and $8. The expected value is:
Half of all potential customers would pay $10 for your product but half would pay $8. Your marginal costs are $4. If you set the price at $10, the expected profit is:
Half of all potential customers would pay $10 for your product but half would pay $8. Your marginal costs are $4. If you set the price at $10, the expected profit is:
A movie executive must decide to fund a new movie project. A success would earn $20 million and a failure would cost $60 million in lost profits. At what probability of expected success should he fund the movie?
A movie executive must decide to fund a new movie project. A success would earn $20 million and a failure would cost $60 million in lost profits. At what probability of expected success should he fund the movie?
A pharmaceutical company must decide whether to fund a new drug development project. A success would earn $10 million and a failure would cost $90 million. At what probability of expected success should she fund the project?
A pharmaceutical company must decide whether to fund a new drug development project. A success would earn $10 million and a failure would cost $90 million. At what probability of expected success should she fund the project?
Which types of poor decisions are more visible to a decision maker's supervisor?
Which types of poor decisions are more visible to a decision maker's supervisor?
The key distinction between risk and uncertainty is:
The key distinction between risk and uncertainty is:
The expected value of a gamble that pays $10 with probability 0.2 and -$4 with probability 0.8 is:
The expected value of a gamble that pays $10 with probability 0.2 and -$4 with probability 0.8 is:
You want to run a difference-in-difference experiment with a price increase for your lawn chairs in Miami. If you are worried about the 'representativeness' of your control group, a good comparison city would be:
You want to run a difference-in-difference experiment with a price increase for your lawn chairs in Miami. If you are worried about the 'representativeness' of your control group, a good comparison city would be:
You want to run a difference-in-difference experiment with a price increase for the bacon cheeseburger item on your menu. If you are worried about 'leakage' with your control group, a good comparison menu item would be:
You want to run a difference-in-difference experiment with a price increase for the bacon cheeseburger item on your menu. If you are worried about 'leakage' with your control group, a good comparison menu item would be:
A false positive is:
A false positive is:
A false negative is:
A false negative is:
We worry that false negatives occur too often relative to false positives due to:
We worry that false negatives occur too often relative to false positives due to:
What are the Type I and Type II error costs?
What are the Type I and Type II error costs?
Based on expected error costs, you should fund a project if it has better than what percentage chance of success?
Based on expected error costs, you should fund a project if it has better than what percentage chance of success?
What should you do if the average probability from studies is less than your threshold for funding?
What should you do if the average probability from studies is less than your threshold for funding?
When devising a strategy with considerable uncertainty, what is the recommended approach?
When devising a strategy with considerable uncertainty, what is the recommended approach?
What is the expected value of an uncertain outcome calculated as?
What is the expected value of an uncertain outcome calculated as?
What should you consider if your uncle offers you a deal with an expected value much greater than the cost?
What should you consider if your uncle offers you a deal with an expected value much greater than the cost?
If you calculate the expected value of option A is greater than option B by 0.013%, what is your likely course of action?
If you calculate the expected value of option A is greater than option B by 0.013%, what is your likely course of action?
When deciding whether to sell widgets for $5 or $6, which price yields higher profits?
When deciding whether to sell widgets for $5 or $6, which price yields higher profits?
You might increase your profits by:
You might increase your profits by:
Selection bias occurs because:
Selection bias occurs because:
Why are randomized experiments considered the 'gold standard'?
Why are randomized experiments considered the 'gold standard'?
What is the key determinant of a careful observational study?
What is the key determinant of a careful observational study?
If you reject a correct hypothesis, what error are you committing?
If you reject a correct hypothesis, what error are you committing?
A manager will decide to fund too few projects if:
A manager will decide to fund too few projects if:
What is the difference between risk and uncertainty?
What is the difference between risk and uncertainty?
How can you deal with uncertainty effectively?
How can you deal with uncertainty effectively?
What is the expected value of guessing on a multiple-choice test with five options?
What is the expected value of guessing on a multiple-choice test with five options?
What is the expected value of NPV when considering a new store with different probabilities?
What is the expected value of NPV when considering a new store with different probabilities?
What is the expected profit or loss from adding a new manufacturing line with varying probabilities?
What is the expected profit or loss from adding a new manufacturing line with varying probabilities?
What is the expected NPV of a viral mobile app investment?
What is the expected NPV of a viral mobile app investment?
What is the minimum probability of success required to invest in a project with an NPV of $75 million?
What is the minimum probability of success required to invest in a project with an NPV of $75 million?
What do you estimate the referrals per dollar are through agency A?
What do you estimate the referrals per dollar are through agency A?
What is the probability that a random customer will use the coupon if 90 out of 3,000 responded?
What is the probability that a random customer will use the coupon if 90 out of 3,000 responded?
What are the expected error costs of shutting down process B first?
What are the expected error costs of shutting down process B first?
What price maximizes expected revenue if 40% value it at $10 and 60% at $6?
What price maximizes expected revenue if 40% value it at $10 and 60% at $6?
You should enter the market if you believe the probability that the incumbent will price low is less than what percentage?
You should enter the market if you believe the probability that the incumbent will price low is less than what percentage?
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Study Notes
Random Variables and Expected Value
- A random variable can take on different values.
- The expected value is calculated as the sum of the products of probabilities and outcomes.
Expected Value in Gamble Scenarios
- If winning $1 on heads and losing $1 on tails, expected value is $0.
- Winning $2 on heads and losing $1 on tails results in an expected value of $0.50.
- Winning $3 on heads and losing $1 on tails leads to an expected value of $1.00.
Investment Decisions
- Comparing projects A and B indicates investing in project A is favorable when A's expected success probability is 0.7.
- If project A has a 0.5 probability of success, it's indeterminate if A or B should be chosen.
Calculating Expected Values
- For three equally likely outcomes with payoffs of $3, $6, and $9, the expected value is $6.
- The expected value of four payoffs of $2, $4, $6, and $8 is $5.
Profit Calculations
- If high-value customers pay $200 and low-value customers pay $175, expected profit per customer is $75 when marginal costs are $100.
Experiment Methodologies
- Difference-in-difference estimates compare changes in outcomes between treatment and control groups to assess effects like price changes or advertising increases.
Cost-Benefit Analyses
- For decisions such as funding projects with expected success, funding is justified when the probability exceeds specific thresholds (e.g., 0.75 for a movie project).
Error Types in Hypotheses
- A "false positive" occurs when a hypothesis is incorrectly accepted.
- Conversely, a "false negative" is the incorrect rejection of a hypothesis.
Risk and Uncertainty
- Risk is quantifiable, while uncertainty involves unknown potential outcomes and their probabilities.
Managerial Decisions
- An inclination to avoid false positives often influences managerial decision-making patterns.
- Decisions made by managers may be influenced by the perceived visibility of outcomes, with major decisions likely scrutinized more heavily.
Strategies for Uncertainty
- In uncertain situations, develop flexible strategies that allow for improvisation rather than rigid plans that fail to adapt to unforeseen events.
Calculation Framework
- The expected value is derived from summing the product of probabilities and their associated values to inform decision-making.### Project Valuation Considerations
- Valuation may underestimate project value in worst-case scenarios.
- Success likelihood of the deal may be overvalued.
Decision-Making in Expected Values
- If the expected value of option A is only slightly higher than option B, it’s reasonable to flip a coin instead of choosing definitively.
Pricing Strategies for Widgets
- Selling at $5 and $6 with a marginal cost of $3 leads to equal profits due to different success rates.
- Higher profits may be achieved by strategically pricing at $6 with a discount when negotiations stall.
Understanding Selection Bias
- Selection bias arises from systematic differences between treatment and control groups impacting outcomes.
Importance of Randomized Controlled Experiments
- These experiments eliminate selection bias, ensuring no systematic differences affect treatment and control groups.
Observational Study Quality
- A strong observational study must ensure the control group mirrors the treatment group without systematic differences.
Hypothesis Testing Errors
- Rejecting a true hypothesis results in a Type I error, indicating a false positive.
Project Funding Decisions
- Managers may underfund uncertain projects due to known failures, lack of exposure to passed opportunities, and inadequate review processes.
Risk vs. Uncertainty
- Neither risk nor uncertainty is accurately explained by typical definitions; they are distinct concepts in decision analysis.
Flexibility in Uncertain Situations
- Strategies should incorporate flexibility to adapt to unforeseen contingencies.
Expected Value in Random Guessing
- Random guessing on a multiple-choice test results in an expected value of zero, considering correct and incorrect answers.
Valuation of New Store Opportunities
- The expected NPV for a new store considering varying population growth scenarios is estimated at $4 million.
Expected Profit/Loss Calculation
- A new manufacturing line could yield an expected gain of $47,000 based on calculated probabilities.
NPV of a New Mobile App Investment
- Expected NPV for a mobile app, factoring in probability of success and failure scenarios, results in an NPV of zero.
Investment Decision Threshold
- For a project with potential NPVs of $75 million and -$25 million, a minimum success probability of 25% is necessary for investment justification.
Referral Effectiveness in Advertising
- Agency A provides an estimated 1.1 referrals per dollar spent, based on increased ad spend and changes in referrals.
Probability of Coupon Usage
- In a customer list of 3,000, the probability of coupon usage is 3%, based on past response rates.
Error Costs in Process Investigation
- Investigating process A first has expected error costs of $16,000 versus lower costs for process B.
Pricing for Maximum Revenue
- The optimal price to maximize expected revenue is $6, catering to varying buyer valuations.
Market Entry Considerations
- Entering a market is justifiable if there is a belief that the incumbent’s likelihood of pricing low is below 75%.
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