http://www.vox.com/cards/crime-rate-drop/crime-rate
I thought this was a very good compilation of the various proposed reasons for the huge drop in crime in the 90s, and some debate for and against each.
Saturday, January 30, 2016
Friday, January 29, 2016
Listen to Wikipedia
http://listen.hatnote.com/
Listen to the sound of Wikipedia's recent changes feed. Bells indicate additions and string plucks indicate subtractions. Pitch changes according to the size of the edit; the larger the edit, the deeper the note. Green circles show edits from unregistered contributors, and purple circles mark edits performed by automated bots. You may see announcements for new users as they join the site, punctuated by a string swell.
Sunday, January 10, 2016
Powerball Odds
So there is a lot of Powerball talk, and I am again intrigued by the possibility of a positive expected value for a lottery. If you remember I wrote a post about Megamillions a few years ago, when the jackpot grew to $640 million. The result, after taking into account both taxes and multiple winners, was that it still wasn't worth playing. I decided to quickly do the same thing for this latest Powerball jackpot.
In a separate post, I made a model to predict the ticket sales based on jackpot amount. This was quite a bit of work, so I'm not doing that here. I'm just going to use the data for the latest drawing (Jan 9th, 2016) to see if that one drawing had a positive expected value in retrospect.
To begin, the expected value of the non jackpot prizes is $0.32, or about $0.28 if you include tax on the $50,000 and $1,000,000 prizes. Note here, I'm ignoring the "Power Play" thing, which increases the payout for the nonjackpot prizes, but costs an extra $1.
Now we need to look at the jackpot. The estimated upfront payout was $587,662,740. After taxes that's $340,844,389. The odds for Powerball recently got way harder, which is why this jackpot is so large. This drawing had 440,321,172 tickets sold. Doing the Poisson distribution we see the probability of various numbers of winners based on the odds and tickets sold:
The odds for no winners (which is what happened) was 22%. This is due to the much lower odds of a jackpot in general.
Adding up the adjusted jackpot shares gives a total of $176,335,787. This could be thought of as the true jackpot value after adjusting for taxes and the possibility of splitting the jackpot. Multiplying by the odds of winning gives an expected value for the jackpot of $0.6035. Adding the nonjackpot expected value gives a total Powerball expected value of $0.88. The ticket costs $2, so it's not even half the value.
Some thoughts: The odds were just increased in Oct 2015, and this is the first huge jackpot after that change. More will follow, so it is possible that the expected value will improve as people get over the hype of a billion dollar jackpot. However, it is worth noting that even if the jackpot doubled, and ticket sales remained constant the expected value would still be below the ticket price.
I haven't gone into details for the math here. The calculations and commentaries are the same as the Megamillions post. So please see that for more discussion.
In a separate post, I made a model to predict the ticket sales based on jackpot amount. This was quite a bit of work, so I'm not doing that here. I'm just going to use the data for the latest drawing (Jan 9th, 2016) to see if that one drawing had a positive expected value in retrospect.
To begin, the expected value of the non jackpot prizes is $0.32, or about $0.28 if you include tax on the $50,000 and $1,000,000 prizes. Note here, I'm ignoring the "Power Play" thing, which increases the payout for the nonjackpot prizes, but costs an extra $1.
Now we need to look at the jackpot. The estimated upfront payout was $587,662,740. After taxes that's $340,844,389. The odds for Powerball recently got way harder, which is why this jackpot is so large. This drawing had 440,321,172 tickets sold. Doing the Poisson distribution we see the probability of various numbers of winners based on the odds and tickets sold:
| 0 | 22.1594% |
| 1 | 33.3922% |
| 2 | 25.1595% |
| 3 | 12.6377% |
| 4 | 4.7610% |
| 5 | 1.4349% |
| 6 | 0.3604% |
| 7 | 0.0776% |
| 8 | 0.0146% |
| 9 | 0.0024% |
| 10 | 0.0004% |
| 11 | 0.0001% |
| 12 | 0.0000% |
| 13 | 0.0000% |
| 14 | 0.0000% |
| 15 | 0.0000% |
The odds for no winners (which is what happened) was 22%. This is due to the much lower odds of a jackpot in general.
Adding up the adjusted jackpot shares gives a total of $176,335,787. This could be thought of as the true jackpot value after adjusting for taxes and the possibility of splitting the jackpot. Multiplying by the odds of winning gives an expected value for the jackpot of $0.6035. Adding the nonjackpot expected value gives a total Powerball expected value of $0.88. The ticket costs $2, so it's not even half the value.
Some thoughts: The odds were just increased in Oct 2015, and this is the first huge jackpot after that change. More will follow, so it is possible that the expected value will improve as people get over the hype of a billion dollar jackpot. However, it is worth noting that even if the jackpot doubled, and ticket sales remained constant the expected value would still be below the ticket price.
I haven't gone into details for the math here. The calculations and commentaries are the same as the Megamillions post. So please see that for more discussion.
Thursday, December 24, 2015
DAC and ADC explanation
https://www.youtube.com/watch?v=cIQ9IXSUzuM
This is a good video that explains how audio signals are sampled and represented digitally, and what effect that has on the final analog output.
This is a good video that explains how audio signals are sampled and represented digitally, and what effect that has on the final analog output.
Thursday, December 17, 2015
Monday, December 14, 2015
Sunday, December 13, 2015
Sunday, November 29, 2015
Thursday, November 19, 2015
Saturday, October 17, 2015
Big Mac Index
https://en.wikipedia.org/wiki/Big_Mac_Index#Manipulation
The big mac index is a quick attempt at explaining purchasing power parity. The idea being that simply knowing the exchange rate is not enough to know how valuable your money from one country will actually be when you try to purchase actual goods there.
Here is the fun part though:
The big mac index is a quick attempt at explaining purchasing power parity. The idea being that simply knowing the exchange rate is not enough to know how valuable your money from one country will actually be when you try to purchase actual goods there.
Here is the fun part though:
Critics of the presidency of Cristina Fernández de Kirchner in Argentina and many economists believe that the government has for years falsified consumer price data to understate the country's true inflation rate. The Economist stated in January 2011 that Big Mac index "does support claims that Argentina’s government is cooking the books. The gap between its average annual rate of burger inflation (19%) and its official rate (10%) is far bigger than in any other country." That year the press began reporting on unusual behavior by the more than 200 Argentinean McDonald's restaurants. They no longer prominently advertised Big Macs for sale and the sandwich, both individually and as part of value meals, was being sold for an unusually low price compared to other items. Guillermo Moreno, Secretary of Commerce in the Kirchner government, reportedly forced McDonald's to sell the Big Mac at an artificially low price to manipulate the country's performance on the Big Mac index. In June 2012, the price of the Big Mac value meal suddenly rose by 26%, closer to that of other meals, after The Economist, The New York Times, and other media reported on the unusual pricing. A Buenos Aires newspaper stated "Moreno loses the battle".
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