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Suppose That a Bag Holds 3 Blue Balls and One

question 17

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Suppose that a bag holds 3 blue balls and one red ball. We pull a ball from the bag at random, return it and then repeat the process. Suppose we continue pulling balls until the blue ball is drawn and then we observe the number of consecutive red balls drawn. What is the average number of red balls between occurrences of blue balls? Is E(X)=n=1n3n4n+1=14n=1n(34)n=3E ( X ) = \sum _ { n = 1 } ^ { \infty } n \frac { 3 { n } } { 4 ^ { n + 1 } } = \frac { 1 } { 4 } \sum _ { n = 1 } ^ { \infty } n \left( \frac { 3 } { 4 } \right) ^ { n } = 3 correct?

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Federal Reserve

The central banking system of the United States, responsible for monetary policy, including regulation of money supply and interest rates.

U.S. Government Securities

Financial instruments issued by the U.S. Treasury or federal government agencies to finance government spending and obligations.

Assets Component

Parts or elements that make up the total value of assets owned by an individual or organization.

Money Supply

The money supply is the total amount of monetary assets available in an economy at a specific time, including cash, coins, and balances held in checking and savings accounts.

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