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Let X denote the outcome when a fair die is rolled. Then ?

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 3E Chapter 5.8

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 3E

Problem 3E

Let X denote the outcome when a fair die is rolled. Then μ = 7/2 and σ2 = 35/12. Note that the maximum deviation of X from μ equals 5/2. Express this deviation in terms of the number of standard deviations; that is, find k, where = 5/2. Determine a lower bound for P(|X − 3.5| < 2.5).

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MacroEcon. - Monetary Policy 03/21/2016 ▯ Monetary Policy  Actions that the Federal Reserve System takes to change interest rates and the money supply  Aim is to affect the economy: GDP, Employment, inflation ▯ ▯ How does monetary policy affect interest and A.D. (Aggregate demand) ▯ ▯ Central banking system  Federal Reserve o 1873-1907: Four severe banking panics o 12 central (regional) banks  Technically a corporation  Stockholders: member banks  Most profit turned over to US treasury every year ▯ ▯ Board of Governors (7 members)  Nominated by President, approved by senate, and serve a 14 year term making $100,000s a year.  Chairperson serves 4-year term: Janet Yellen ▯ ▯ “The Fed”  Independent from the rest of the government  Chairperson makes a statement to the senate about every month regarding the fed’s standing  Sole responsibility: monetary policy to affect the economy for the better  1978-present, the fed has had the responsibility to promote a positive economy ▯ ▯ Federal Open Market Committee (FOMC)  Made up of the 7 members of the Board of Governors  Janet Yellen is the chair  4 (of 11) regional bank presidents are members ▯ Short term interest rates and size of money supply is what they have a LARGE impact on ▯ ▯ Central bank independence  Bank’s ability to make decision without political interference  Proponents: independence keeps politics out o Fed can take longer term view o Maintain low/stable inflation  Opponents: “independence is Undemocratic” ▯ ▯ ***Open-market operations  Every day the market is open, the fed is playing games with us, buying and selling treasury bills.  Treasury bills: Debt instruments with a maturity of one-year or less ▯ What does the FOMC do if it wants to lower interest rates  Purchase treasury bills from the banks  Pays for them with newly created bank reserves What is the difference when the Fed buys treasury bills from the banks as opposed to you or me Market for bank reserves  Supply of reserves is determined by federal reserve policy  Demand for reserves determined o Banks since they are required to hold reserves o Requires reserves = m x D (Transaction deposits) o But the demand for D depends on the volume of transactions o Which depends on real GDP and the price level  Interest rate: federal funds rate Federal funds rate  Interest rates that applies when banks borrow reserves from one another Why is there a reserve market  Some banks may be short of reserves or have excess reserves and would need to buy or sell them How the fed lowers the federal funds rate  Purchase t-bills  Supply of reserves will increase, moving the interest rates down Bond prices and interest rates  Higher bond prices will cause interest rates to fall o Bonds pay a fixed amount per year o Bond that sells for $1,000 with 6% interest rate, have to make a $60 payments o If price of the bond rises to $1,200, the interest rate goes down to 5% o It is an INVERSE relationship Expansionary Policy  Fed wants money supply to increase; interest rates to fall, so…  They make an open market purchase. Banks excess reserves will…  Increase, so the money supply expands.  By buying bonds, the fed causes the prices of bonds to…  Increase so interest rates decrease Contractionary policy  Fed wants money supply to decrease; interest rates to rise, so…  They make an open market SALE. Banks excess reserves will…  Decrease, so money supply contracts  By selling bonds, the Fed causes the prices of bonds to…  Decrease so interest rates INCREASE Which interest rate  Fed “controls” federal funds rate and the treasury bills rate  Fed can “influence” other interest rates: credit cards, auto loans, etc.  Normally, interest rates tend to move TOGETHER  During financial crisis relationship broke down

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Chapter 5.8, Problem 3E is Solved
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Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Let X denote the outcome when a fair die is rolled. Then ?