Month: February 2022

THE DARTH VADER RULE

Mary Pat Campbell

Link:https://www.sav.sk/journals/uploads/1030150905-M-O-W.pdf

doi: : 10.2478/v10127-012-0025

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Excerpt:

In life insurance mathematics, the concept of a survival function is commonly
used in life expectancy calculations. The survival function of a random variable X
is defined at x as the probability that X is greater than a specific value x. For
a non-negative random variable whose expected value exists, the expected value
equals the integral of the survival function. We propose to designate this result
as the Darth Vader Rule1. It holds for any type of random variable, although its
most general form relies on the integration by parts formula for the Lebesgue-
-Stieltjes integral, fully developed by H e w i t t [3]. This result, while known (and
stated in F e l l e r [1]), is not widely disseminated except in life insurance mathematics texts; but it is worth knowing and popularizing because it provides an
efficient tool for calculation of expected value, and gives insight into a property
common to all types of random variables.
We give a proof of the Darth Vader Rule which works for all random variables which are non-negative almost surely and whose expected value exists.
The proof is based not on the Lebesgue integral formulation of [3], but on the
generalized Riemann integration of H e n s t o c k and K u r z w e i l [2], [4]. Since
every Lebesgue integrable function is also generalized Riemann integrable, the
proof here includes all cases covered by [3].
While the result is simple to state and comprehend, its proof using Lebesgue
integral theory is somewhat complex.

Author(s): Pat Muldowney — Krzysztof Ostaszewski — Wojciech Wojdowski

Publication Date: 2012

Publication Site: Tatra Mountains Mathematical Publications

An Epidemic of Bad Budgeting

Mary Pat Campbell

Link: https://www.city-journal.org/covid-19-lockdowns-exposed-cities-deep-seated-financial-troubles

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The past year has been a fiscal nightmare for Nashville. Covid-19 helped punch a $332 million hole in the city’s $2.46 billion budget. Tennessee state comptroller Justin Wilson warned that, without drastic action, the state might take over management of Nashville’s affairs. In response, the city council raised property taxes 34 percent, spurring a citizen revolt in the form of a ballot initiative to overturn the tax hike. Without the extra revenue, however, Mayor John Cooper’s administration said that drastic cuts would be unavoidable: “Few corners of the Metro government, including emergency services and schools, would be spared significant reductions or eliminations.”

Nashville’s budget woes predate the pandemic: the city began borrowing money to cover deficits after the Great Recession of 2008–09. City leaders, at the same time, went into heavy debt to build new government-owned attractions, offered workers health retirement benefits that they haven’t funded, and deep-sixed pension reforms that saved the state billions of dollars. In fact, back in December 2019, the state comptroller issued a similar warning to Nashville about its shaky finances.

The Music City isn’t alone. The Covid health emergency and accompanying economic downturn caused budget crises for municipalities—cities, counties, and school districts—across America. A February letter from 400 mayors to President Biden said that the pandemic-inflicted strain on municipal budgets had “resulted in budget cuts, service reductions, and job losses” throughout local government. America’s largest city, New York, grappled with a nearly $10 billion budget deficit in the spring of 2020, while Chicago struggled with a $2 billion gap. Dozens of local governments used the crisis to justify budget maneuvers that fiscal experts generally frown upon, from borrowing money to close deficits to issuing bonds to fund employee pensions.

Author(s): Steven Malanga

Publication Date: Summer 2021

Publication Site: City Journal

U.S. Has Far Higher Covid Death Rate Than Other Wealthy Countries

Mary Pat Campbell

Link:https://www.nytimes.com/interactive/2022/02/01/science/covid-deaths-united-states.html

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Excerpt:

“We’ve finally started getting to a stage where most of the population has been exposed either to a vaccine or the virus multiple times by now,” said Dr. David Dowdy, an epidemiologist at the Johns Hopkins Bloomberg School of Public Health. Referring to American and European death rates, he continued, “I think we’re now likely to start seeing things be more synchronized going forward.”

Still, the United States faces certain steep disadvantages, ones that experts worry could cause problems during future Covid waves, and even the next pandemic. Many Americans have health problems like obesity and diabetes that increase the risk of severe Covid.

Author(s): Benjamin Mueller and Eleanor Lutz

Publication Date: 1 Feb 2022

Publication Site: NYT