Problem of the Week: A betting puzzle

QUESTION: A gambler playing against the “house” in a game like roulette or slots adopts the rule “Play until you win a certain amount, then stop.”  Will this ensure against player losses? What will be its effect on the house’s profit? ANSWER: Some look at this…

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Problem of the Week: The Second Heads

QUESTION: A friend tosses two coins, and you ask “Is one of them a heads?”  The friend replies “Yes.” What is the probability that the other is a heads? ANSWER:   One-third.  There are four ways the coins could have landed originally: HH:  0.25 probability…

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Problem of the Week: The Value of Bedrooms

Question: You work for an internet real-estate company, building statistical models to predict home price on the basis of square footage, number of bedrooms, number of bathrooms, property type (single family home, townhouse, multiplex), and age. Surprisingly, you find the coefficient for bedrooms is negative,…

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Problem of the Week: Missing Data

Question: You have a supervised learning task with 30 predictors, in which 5% of the observations are missing.  The missing data are randomly distributed across variables and records. If your strategy for coping with missing data is to drop records with missing data, what proportion…

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