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stupid probability questions
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stupid probability questions

  #11 (permalink)
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For more info Checking whether a coin is fair - Wikipedia, the free encyclopedia.
For doing some tests RANDOM.ORG - Coin Flipper.

Take your Pips, go out and Live.
Luke.
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  #12 (permalink)
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AFAIK that a straight binomial thing if it is a fair coin. Google visual attached.

Or did I miss the original question?

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  #13 (permalink)
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Fat Tails View Post

This would be the peak value of the binomial distribution, which approximates the bell curve of the Gauss distribution. The binomial distribution is quite important for option pricing modells. The Cox-Rubinstein model - which is simpler than the Black-Scholes model - relies on the binomial distribution.

Hope I did not get anything wrong here, comments appreciated.

I was going to mention Cox-Rubinstein, but I thought it would be overkill to mention a binomial pricing model when talking about coin flipping.

I think Black-Scholes is easier if you have a CND calculation nearby. I remember I had to do part of a Cox-Rubinstein tree by hand for a test.

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  #14 (permalink)
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Thanks Luke. I found some information below that is off-topic but might have
some use to someone.


Wikipedia has a number of interesting links in the "SEE ALSO" section of Checking_if_a_coin_is_fair.
I eventually ended up here:

Seven states of randomness - Wikipedia, the free encyclopedia

{Extensive excerpt below}

Seven states of randomness

The seven states are:

Proper mild randomness
Borderline mild randomness
Slow randomness with finite delocalized moments
Slow randomness with finite and localized moments
Pre-wild randomness
Wild randomness
Extreme randomness

These seven states were first introduced in by Benoît Mandelbrot in his 1997 book Fractals and scaling in finance which applied fractal analysis to the study of risk and randomness.

Intuitively speaking, Mandelbrot argued that the traditional normal curves do not properly capture empirical and "real world" distributions and there are other forms of randomness that can be used to model extreme changes in risk and randomness. He observed that randomness can become quite "wild" if the requirements regarding finite mean and variance are abandoned. Wild randomness corresponds to situations in which a single observation, or a particular ourcome can impact the total in a very disproportionate way.


Using elements of this theory, in March 2006, a year before the Financial crisis of 2007–2010, and four years before the Flash crash of May 2010, during which the Dow Jones Industrial Average had a 1,000 point intraday swing within minutes, Mandelbrot and Nassim Taleb published an article in the Financial Times arguing that the traditional "bell curves" that have been in use for over a century are inadequate for measuring risk in financial markets, given that such curves disregard the possibility of sharp jumps or discontinuities.[4] Contrasting this approach with the traditional approaches based on random walks, they stated:[5]


We live in a world primarily driven by random jumps, and tools designed for random walks address the wrong problem.

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Thanks to those that responded. I don't know why I asked about this but
it is obviously a more complex matter than I thought. Now I know how
Two-Face feels.


Before his transformation into Two-Face, Harvey Dent was one of the best attorneys in Gotham City, proficient in nearly all matters pertaining to criminal law.

Following his disfigurement, he developed multiple personality disorder, and became obsessed with duality, from staging crimes around the number two to carrying and using dual firearms (such as .22 semiautomatics). Two-Face does things according to chance and therefore leaves all the decisions he makes to fate at the flip of his two-headed coin in an almost obsessive compulsive desire.

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  #16 (permalink)
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stephenszpak View Post
Using elements of this theory, in March 2006, a year before the Financial crisis of 2007–2010, and four years before the Flash crash of May 2010, during which the Dow Jones Industrial Average had a 1,000 point intraday swing within minutes, Mandelbrot and Nassim Taleb published an article in the Financial Times arguing that the traditional "bell curves" that have been in use for over a century are inadequate for measuring risk in financial markets, given that such curves disregard the possibility of sharp jumps or discontinuities.[4] Contrasting this approach with the traditional approaches based on random walks, they stated:[5]

The idea of Gauss distributions (bell curves) is just a model. It heavily relies on the efficient market hypothesis, which assumes that there are noise traders and arbs. Whenever a noisetrader makes a random decision, the arb makes a riskfree profit and puts the market back to its equilibrium. This, of course, is a fairy tale model which continues the tradition of the magical invisible hand of Adam Smith.

I would not call this nonsense, although it comes quite close to it. Economists just have a preference for simple and closed models to explain reality. The noise traders do not make random decisions, but there moves are correlated. The arb traders cannot execute their arbitrage, because often there are no instruments available or the mean reversion path to equilibrium requires further risk exposure.

Mandelbrot is one of the economists who followed the path of empirical studies. By taking price movements from the cotton market, he actually proved that not all price distributions were Gaussian but that some had fat tails. The Chicago boys did not like these news, as all their models - including the Black-Scholes option pricing formula - rely on Gauss distributions. It is known that the nobel prize winners Merton and Scholes had some fun with their mean reversion models a few years later, when LTCM tanked.

This is the good news. Markets are just. Markets would not have rewarded nobel prizes to Merton and Scholes, but to Mandelbrot. But Mandelbrot's ideas were not accetpable, as defined by J.K. Galbraith in his book "The Affluent Society". Cited from the chapter "The Concept of Conventional Wisdom":

"As noted, the hallmark of the conventional wisdom is acceptability. It has the approval of those to whom it is addressed. There are many reasons why people like to hear articulated that which they approve. It serves the ego: the individual has the satisfaction of knowing that other and more famous people share his conclusions. To hear what he believes is also a source of reassurance...."

When will "Behavioral Finance" be followed by "Behavioral Science"? Scientific ideas spread out in a similar way as security prices and trading algorithms. Science also has its fat tails, sudden paradigm shifts as explained by Thomas Kuhn. I believe that the next paradigm will take us closer to Minsky and Mandelbrot than the previous one.

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  #17 (permalink)
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as defined by J.K. Galbraith in his book "The Affluent Society". Cited from the chapter "The Concept of Conventional Wisdom":

"As noted, the hallmark of the conventional wisdom is acceptability. It has the approval of those to whom it is addressed. There are many reasons why people like to hear articulated that which they approve. It serves the ego: the individual has the satisfaction of knowing that other and more famous people share his conclusions. To hear what he believes is also a source of reassurance...."

Or to put it another way:


2 Timothy 4:3,4–”For the time will come when they will not endure sound doctrine; but wanting to have their ears tickled, they will accumulate for themselves teachers in accordance to their own desires; and will turn away from listening to the truth and wander off into myths.”

We're way off topic now (perhaps for the best).

Fat Tails wrote: Scientific ideas spread out in a similar way as security prices...

I read a book a number of years ago called The End of Science.

The End of Science, John Horgan, (9780553061741) Paperback - Barnes & Noble

Excerpt:

If one believes in science, one must accept the possibility—even the probability— that the great era of scientific discovery is over. By science I mean not applied science, but science at its purest and grandest, the primordial human quest to understand the universe and our place in it. Further research may yield no more great revelations or revolutions, but only incremental, diminishing returns.

It wasn't an easy read, but it was interesting. Have you read it?

- Stephen

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  #18 (permalink)
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stephenszpak View Post
I read a book a number of years ago called The End of Science.

The End of Science, John Horgan, (9780553061741) Paperback - Barnes & Noble

Excerpt:

If one believes in science, one must accept the possibility—even the probability— that the great era of scientific discovery is over. By science I mean not applied science, but science at its purest and grandest, the primordial human quest to understand the universe and our place in it. Further research may yield no more great revelations or revolutions, but only incremental, diminishing returns.

It wasn't an easy read, but it was interesting. Have you read it?

- Stephen

Haven't read it yet, might do so. It looks like a controversial, but interesting book. Scientific discovery is not yet over, it just shifts to other places. Sometimes, I have the feeling that in social sciences, scientific discovery has not even fully started. But of course, science is limited, just using a different language to describe what can be seen, heard, smelt and felt.

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My head just exploded. You guys are way smarter than me, I hate math.

Mike

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My head just exploded. You guys are way smarter than me, I hate math.

Mike

Glad you liked it, just copied it from Wikipedia. But with your coding capabilities you should not pretend to be impressed by some basic math.

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