MidLifeCrisis Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by Sven Golly: Sorry, Steve, but your analogy is invalid. Read the Wikipedia post that I linked to above.Sorry Sven but the analysis conducted is based on a false assumption. The probability referenced is based on a confidence factor (hence the term confidence con). It depends on the confidence level you have on the emperical data on hand. If someone were to influence the potential results then this argument would hold true. Unlike the $64,000 question, I don't think this game show is rigged. Thus taken the variables at hand, you are left with two choices, each with the identical potential to hold the winning prize. You can do the math yourself. Reference Link Example of probability density functions The homogeneous distribution on the interval (a,b) is given by http://www.bio.vu.nl/thb/course/tb/tb/img451.gif If is homogeneously distributed on the interval (0,1), is exponentially distributed with parameter 1. The importance of this fact is the readily availability of random generators for homogeneously distributed random variables, which are used in Monte Carlo methods. The beta distribution is defined by http://www.bio.vu.nl/thb/course/tb/tb/img456.gif where and take values in , while . We have , , , . The relationship between the exponential and the Poisson distribution is explained in the section on point processes. The sum of n independent exponentially distributed random variables with a parameter is gamma distributed: http://www.bio.vu.nl/thb/course/tb/tb/img466.gif Steve A Lifetime of Peace, Love and Protest Music www.rock-xtreme.com Link to comment Share on other sites More sharing options...
Phred Posted December 22, 2005 Author Share Posted December 22, 2005 Steve, This appears to be a formula for randomness - which no one is disbuting here... Assuming that the result is behind a random door, you can greatly improve your chances of winning by switching. Because by switching, you are essentially choosing both other doors, versus your door. Did you try my 1000 number example? Does that help? What ifI said, would you switch you 1 door to have what is behind these two doors... Does that help. I'm just saying', everyone that confuses correlation with causation eventually ends up dead. Link to comment Share on other sites More sharing options...
MidLifeCrisis Posted December 22, 2005 Share Posted December 22, 2005 I'll bow out of this discussion here... * leaves grumbling and wondering why he spent 6 years getting a masters degree in math only to be refuted by WiKiPedia * Steve A Lifetime of Peace, Love and Protest Music www.rock-xtreme.com Link to comment Share on other sites More sharing options...
Sven Golly Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by MidLifeCrisis: Sorry Sven but the analysis conducted is based on a false assumption. Which, mine or yours? Just kidding... but I'm not sure what your last message was meant to convey. The argument you posted is valid for your coin toss analogy, but not in the 3 door problem (also note that this isn't a con, such as in 3-card monte). Of course, if you're capitulating, then I'll put down the bat and walk away from this poor equine beast who expired a few hours ago, and grab myself another rum'n'egg nog. Cheers, SG Link to comment Share on other sites More sharing options...
MidLifeCrisis Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by Sven Golly: The argument you posted is valid for your coin toss analogy, but not in the 3 door problem (also note that this isn't a con, such as in 3-card monte). I'll just agree to disagree at this point. I certainly don't want to beat the animal to death either. Now if we were arguing over the changes to Hang on Sloopy that would be a cause worth fighting for. Steve A Lifetime of Peace, Love and Protest Music www.rock-xtreme.com Link to comment Share on other sites More sharing options...
Garrafon Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by MidLifeCrisis: Originally posted by Sven Golly: The argument you posted is valid for your coin toss analogy, but not in the 3 door problem (also note that this isn't a con, such as in 3-card monte). I'll just agree to disagree at this point. I certainly don't want to beat the animal to death either. Now if we were arguing over the changes to Hang on Sloopy that would be a cause worth fighting for. This issue has already been beaten to death among math wonks I think the consensus is, if the host knows where the Oasys is, then the odds are greater by switching, but if does not, then Steve's randomness theory is correct and the odds are not improved by switching. The key lies in implicit information gained if the host knows where the Oasys is. Link to comment Share on other sites More sharing options...
MidLifeCrisis Posted December 22, 2005 Share Posted December 22, 2005 Very well put Garrafon. I think I actually concured on this at one point. If the host has any intention of influencing the outcome (good or bad) than I 100% agree with the concensus. Steve A Lifetime of Peace, Love and Protest Music www.rock-xtreme.com Link to comment Share on other sites More sharing options...
JeffLearman Posted December 22, 2005 Share Posted December 22, 2005 It has nothing to do with the host intentionally influencing things -- the host follows rigid rules. He just knows which is the door with the prize, and will never open that door. That constitutes information, and in many cases that information is revealed. It's revealed in any case where you didn't pick the right door in the first place. But your post about 6 years as a math major makes me feel better. Poetry and probability were the only subjects that ever made me feel stoopid! And this problem really stumped me until I gave it a lot of careful thought (and new the correct answer ...) Link to comment Share on other sites More sharing options...
MidLifeCrisis Posted December 22, 2005 Share Posted December 22, 2005 knows which is the door with the prize, and will never open that door == influencing Why can't I just let this go....I hate being anal retentive sometimes... Steve A Lifetime of Peace, Love and Protest Music www.rock-xtreme.com Link to comment Share on other sites More sharing options...
Sven Golly Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by MidLifeCrisis: knows which is the door with the prize, and will never open that door == influencing Agreed... but that is the whole premise... the deliberate revealing of a goat- (or Yanni-)concealing door. I will agree that without this, Steve's post gets the upper hand... but that's not the premise. Why can't I just let this go....I hate being anal retentive sometimes... I have no idea what you're talking about (whacking the horse one more time for good luck). Cheers, SG Link to comment Share on other sites More sharing options...
MidLifeCrisis Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by Sven Golly: but that is the whole premise... Then we are in violent agreement The beast can rest in peace now.. Steve A Lifetime of Peace, Love and Protest Music www.rock-xtreme.com Link to comment Share on other sites More sharing options...
Sven Golly Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by MidLifeCrisis: Then we are in violent agreement The beast can rest in peace now.. Damn, I love it when a plan comes together! For this, and in Tom's absence, I hereby raise a toast to violet agreement! Cheers! SG Link to comment Share on other sites More sharing options...
Tusker Posted December 22, 2005 Share Posted December 22, 2005 Originally posted by learjeff: Tusker, I must not have been clear. The odds are NOT 50/50 between your door and the other unopened door. No LJ, I was not clear. Most befuddled in fact. Sorry. I read the Wiki explanation and that helped. It is counter-intuitive and quite elegant whan you stand back from it. Are there other relatively simple counter-intuitive probability tricks like these? This is a great metaphor for change management types to use in arguing for mid-course corrections. Jerry Link to comment Share on other sites More sharing options...
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