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Answer: Let Y1 and Y2 be independent and uniformly

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 95SE Chapter 6

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 95SE

Problem 95SE

Let Y1 and Y2 be independent and uniformly distributed over the interval (0, 1). Find the probability density function of each of the following:

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Chapter 14: Money, Banking, and Financial Institutions Functions of Money  Medium of Exchange o Used to buy/sell goods  Unit account o Goods valued in dollars  Store of Value o Hold some wealth in money form  Money Definition M1 o M1 (cash in your pocket)  Currency  Checkable deposits o M2  M1 plus near-monies  Savings deposits Federal Reserve – Banking System  Historical background (1912)  Different entities of Fed  Board of Governors  Appointed by the President and confirmed by the senate for 14 year non-renewable term  Headquartered in DC  7 governors, one of them is appointed as a chair  12 federal reserve banks o Serve as the central bank o Quasi-public banks o Bankers Bank o NY Fed is the most important  Federal Open Market Committee (FOMC) o 12 voting members, 7 governors plus 5 presidents of district banks  Actually votes on issues, a lot of people attend meetings but only 12 actually vote  Presidents rotate each year on who votes but NY President ALWAYS votes o Makes important monetary policy decisions o Meets about 8 times a year  Meeting schedule is public  Commercial banks and thrifts o 6,800 commercial banks o 8,700 thrifts  Thrifts – kind of commercial banks (credit unions/ loan associations) o Big Four:  BOA – Acquired Merrill Lynch  JP Morgan Chase – Acquired Bear Sterns  Citi Group  Wells Fargo – Acquired Wachovia Bank  Federal Reserve Functions o Issues currency  Regulating money supply in the US  Fed is independent institution that is created by gov’t but separated from the gov’t o Set reserve requirements  Fed mandates every commercial bank to keep fraction of total deposits in reserves (10%) o Lend money to banks (Fed operates discount window) o Collect checks o Act as fiscal agent for US government o Supervise Banks o Control the money supply and influence interest  Federal Reserve Independence o Established by Congress as an independent agency o Protects the Fed from political pressures o Feds policies cannot be reversed o Fed is given a freedom to pursue its own objectives and choose monetary policy tools to do so o Feds objectives  Dual mandate: price stability (2% inflation rate) and maximum and sustainable economic growth o Enables the fed to take actions to increase interest rates in order to stem inflation as needed (can be politically unpopular move) o Political Business Cycle o Opponents: undemocratic, unaccountable, not transparent enough o Dodd-Frank Act: Wall Street Reformation Act of 2010 o GAO Government Audit (accountability) office can audit Fed’s lending programs o Proposal to audit Fed’s monetary policy decisions, didn’t pass  Fed kept it’s independence The Financial Crisis of 2007-09  Mortgage default crisis  Subprime mortgage loans  Mortgage-backed securities  Government programs that encouraged home ownership o Bad incentives provided by mortgage lenders (no credit checks) o Declining real estate values  Securitization – the process of slicing up and bundling groups of loans into new securities  These securities (MBS) ended up everywhere  Insurance companies insured those securities  Sever conflict of interest  Credit Rating Agencies o Moody’s, S&P, Fitch o Ratings vary from D – AAA. Credit rating agencies assigned AAA rating to lots of the MBS. Why Because SP, Moody, and Fitch get paid by the same corporations who issue those securities  When interest rates increased, and real estate values fell, lots of homeowners defaulted on mortgage loans  Defaults happen on massive scale and the system collapsed  Why no one saw it coming o Failure to predict massive defaults across the country o Exposure and interconnected mess of many large financial institutions o Importance of many non-bank institutions (shadow banks) and lack of regulation  Shadow banks: not commercial but act like banks (hedge funds, mutual funds) o Free riding (everyone thought someone else was supposed to do the job) o Insurance (gave false sense of security to investors) o Many securities were traded over-the-counter (no regulations)  Failures and near-failures of financial firms o Countrywide to BOA: second largest lender o Washington Mutual to JPMorgan Chase: largest lender o Wachovia (fourth largest bank) to Wells Fargo  Other firms filed for bankruptcy (Lehman Brothers) Sep. 18, 2008  Troubled Asset Relief Program (TARP) o Allocated $700 billion to make emergency loans o Instead treasury ended up buying stock o Saved several institutions from failure  Fed extensively lent money to financial institutions  If corporation knows that it will always get bailed out by the government, then it has very strong incentives to be reckless Post Crisis US Financial Services  Major categories of financial institutions o Commercial banks o Thrifts o Insurance companies o Pension funds o Securities firms o Investment banks  Consolidation in the industry  Need to know words o Mutual funds: sell shares to large number of small investors and invest funds in diversified portfolio of securities (stocks, bonds, commercial paper) o Security: financial asset (something that promises future stream of income) that’s traded on the financial markets o Stocks: pay dividends, not guaranteed. Varies with company profitability o Bonds: make fixed payments, guaranteed, does not vary o Derivative: promise to deliver certain asset at a specified price at some future date.  For example: Futures -> promise to deliver one gallon of gas at $3 on April 7, 2017 o Investment Bank: financial institutions that provide various services:  Wealth management  Securities trading  Underwriting: helping private start ups go public or helping already established corporations to sell new issues of stock  Guarantee a certain price for a stock and later resell to investors on NYSE or NASDAQ (tech stocks)  Connection between Wall Street and Main Street o Wall street or financial institutions provide necessary funding to al kinds of firms (small, medium-sized, and large corporations) for long-run and day to day operations) o For example: car parts company may take out a loan from a bank to stock its inventories and slowly repay the loan using its sales proceeds. o Or a large corporation may sell a commercial paper to investment bank (or mutual fund), raise millions to purchase necessary equipment and pay employee salaries o Therefore, if Wall Street is unable to make loans to or buy commercial paper from main street the main street cant stock inventories or pay salaries  Credit Crunch o Commercial banks used to be just banks in the past, before 1999  Glass Steagall Act of 1933: separated commercial banking from investment banking and insurance  Some people want to bring Glass Steagall back o Wall Street Reform and Consumer Protection Act (Dodd- Frank Act of 2010)  Passed to help prevent many of the practices that led to the crisis  Major provisions:  Financial stability oversight council o Collection of Fed, FDIC, SEC, Treasury, Comptroller of currency, others)  Living will of SIFIs (Systematically important financial institution)  More securities traded on public exchanges  Retaining credit risk  Critics say it adds heavy regulatory costs

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Chapter 6, Problem 95SE is Solved
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Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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Answer: Let Y1 and Y2 be independent and uniformly