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 09-30-2009, 12:11 AM #126 Englanese stranger   Join Date: Oct 2008 Location: Calgary, Alberta Posts: 11 Re: The Official Math/Physics/Whatever Homework questions thread I am in a beginner game theory course and I am having some trouble when it comes to games that involve more than 3 players. I don't understand how to set up the games in strategic form and I was wondering if someone could help me out. One of my home work questions is: Suppose several friends go out to dinner with the understanding that the bill will be divided equally. The problem is that someone might order something expensive, knowing that part of the cost will be paid by others. To analyze the situation, suppose there are n diners and for simplicity they have the same food preferences. The accompanying table states the price of each of three dishes on the menu and how much each person values it. Value is measured by the maximum amount the person would be willing to pay for the meal. dish value price surplus pasta \$21 \$14 \$7 salmon \$26 \$21 \$5 steak \$29 \$30 -\$1 a) suppose there are two diners. What will they order (at a Nash equilibrium)? b)suppose there are four diners. What will they order (at a Nash equilibrium)? I solved question a) no problem and got (salmon, salmon) but I have absolutely no idea how to do question b). I know this forum has a rule to try it yourself but I honestly don't know where to start.
 09-30-2009, 12:26 AM #127 furyshade Carpal \'Tunnel     Join Date: Apr 2006 Location: Pasadena, CA Posts: 10,138 Re: The Official Math/Physics/Whatever Homework questions thread Let A;B;C;D be sets in some universal set u. Assume that A U B = u = C U D and A - C = null set. Prove that u = B U D. i can get that A is a sub set of C so C U B = u but can't seem to get how you get that to C U D = u. i feel it has something to do with subtracting the absolute compliment of C from D but not really sure.
09-30-2009, 01:26 AM   #128
lastcardcharlie
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by furyshade Let A;B;C;D be sets in some universal set u. Assume that A U B = u = C U D and A - C = null set. Prove that u = B U D.
Counter-example: A = 1, 2; B = 3, 4; C = 1, 2, 3; D = 4.

09-30-2009, 01:35 AM   #129
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Re: The Official Math/Physics/Whatever Homework questions thread

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 Originally Posted by lastcardcharlie Counter-example: A = 1, 2; B = 3, 4; C = 1, 2, 3; D = 4.
it isn't just saying A U B = C U D, it is saying that A U B = u = C U D, where u is the set of all possible elements. from the book it seems this is a naive set theory problem so basically we are allowed a set of all sets. so basically A U u = u and A intersection U = A. basically A is some set of elements and B is at least all the elements not in B, same with C and D.

 09-30-2009, 05:17 PM #130 furyshade Carpal \'Tunnel     Join Date: Apr 2006 Location: Pasadena, CA Posts: 10,138 Re: The Official Math/Physics/Whatever Homework questions thread disregard my question, the professor emailed out a correction on the problem and it is really easy. for anyone interested it is A intersection C = null not A - C = null
 10-02-2009, 04:34 AM #131 Reefypoopoo banned     Join Date: Nov 2007 Location: ninny rubbin' Posts: 8,630 Re: The Official Math/Physics/Whatever Homework questions thread drinking game question: I pull one card, opponent pulls 2 cards from a deck. Highest card of the 3 wins, loser drinks once. Either of opponents cards can win. What % of the time am I drinking?
 10-02-2009, 05:12 AM #132 Pyromantha veteran   Join Date: Dec 2007 Posts: 2,227 Re: The Official Math/Physics/Whatever Homework questions thread 2/3
 10-02-2009, 05:16 AM #133 Reefypoopoo banned     Join Date: Nov 2007 Location: ninny rubbin' Posts: 8,630 Re: The Official Math/Physics/Whatever Homework questions thread lmao that was so incred easy once I thought about it for 3 secs. Thx
 10-02-2009, 05:40 AM #134 goblinhat adept     Join Date: Sep 2007 Posts: 883 Re: The Official Math/Physics/Whatever Homework questions thread Quite a broad question. If you were to pick one scientific breakthrough in physics which had a large impact on other topics in physics research and other engineering areas. Which would be easy to discuss what would you pick?
 10-02-2009, 04:12 PM #135 Reefypoopoo banned     Join Date: Nov 2007 Location: ninny rubbin' Posts: 8,630 Re: The Official Math/Physics/Whatever Homework questions thread
 10-03-2009, 10:55 PM #136 Jim Ickaccount journeyman   Join Date: Oct 2008 Posts: 219 Re: The Official Math/Physics/Whatever Homework questions thread How do I solve for x in the following equation? 100 * 1.02 ^ x = 1000 * 1.01 ^ x
10-04-2009, 01:54 AM   #137
Myrmidon7328
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Jim Ickaccount How do I solve for x in the following equation? 100 * 1.02 ^ x = 1000 * 1.01 ^ x
1. Divide both sides by 100
2. Take the natural logarithm of both sides

xln(1.02) = ln(10)+xln(1.01)

solve for x.

 10-04-2009, 06:13 AM #138 henrix77 centurion   Join Date: Dec 2005 Posts: 164 Re: The Official Math/Physics/Whatever Homework questions thread Have a question for the collective math/statistics genii... Assume I am playing a slot machine with an expected aggragate payout percentage of 95%. Each spin costs me \$10, and I must wager a grand total of \$300,000. I of course realize that my expected loss is \$15,000. However, what are my chances of losing \$20,000, \$25,000...etc.? Conversely, what are my chances of actually coming out ahead? Is it possible to figure out these expectations without knowing the exact paytable and odds for each winning combination (in other words, is knowing just the overall EV enough)? I'd be very interested to know what the odds are for falling within certain win/loss ranges, and more importantly, how this is calculated. Thanks to anyone who contributes.
10-04-2009, 06:51 AM   #139
Pyromantha
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by henrix77 Have a question for the collective math/statistics genii... Assume I am playing a slot machine with an expected aggragate payout percentage of 95%. Each spin costs me \$10, and I must wager a grand total of \$300,000. I of course realize that my expected loss is \$15,000. However, what are my chances of losing \$20,000, \$25,000...etc.? Conversely, what are my chances of actually coming out ahead? Is it possible to figure out these expectations without knowing the exact paytable and odds for each winning combination (in other words, is knowing just the overall EV enough)? I'd be very interested to know what the odds are for falling within certain win/loss ranges, and more importantly, how this is calculated. Thanks to anyone who contributes.
You cannot estimate these without knowing the paytable.

Consider two concrete examples.

1) A spin costs you \$10, 1 time in a million you win 9.5 million dollars, all other times you lose your \$10. Then your expected loss over 30,000 spins is \$15,000, but the most common result after 30,000 spins is to have lost \$300,000. The chances of you losing over \$25,000 is the same as the chances of you losing over \$1 - both occur if you fail to hit the 'jackpot'. This happens (999999/1000000)^30000 = 97% of the time.

2) A spin costs you \$10. Every time you get back \$9.50. Then your expected lost is still \$15,000, and the most common result after 30,000 spins is to have lost \$15,000. It is impossible that you lose over \$25,000. This game is extremely boring to play

Obviously those were extreme and trivial examples, but the point is to show that the EV of a spin is not enough to answer your questions. You also need to know the variance of a spin, at which point you can use the central limit theorem as the number of spins is so large. It seems to me that to calculate the variance you would need the exact paytable.

If this relates to bonus-whoring then you should choose the machine with the smallest variance to maximize your utility. The machine with the smallest variance will tend to be one that pays out relatively frequently with relatively small prizes, rather than one which has a large jackpot which is rarely hit.

 10-04-2009, 11:42 PM #140 3kingme3 old hand     Join Date: Mar 2008 Location: dont google me Posts: 1,483 Re: The Official Math/Physics/Whatever Homework questions thread ok I need some help please on this calc work, trying to evaluate a derivative and I cant use the shortcut f(x)= x+radical(x) I started by using lim as h ->0 is (f(x+h)-f(x))/h and have gotten it down to (h+radical(x+h)-radical(x))/h but Im stuck now... Whats my next step?
10-05-2009, 12:24 AM   #141
thylacine
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by 3kingme3 ok I need some help please on this calc work, trying to evaluate a derivative and I cant use the shortcut f(x)= x+radical(x) I started by using lim as h ->0 is (f(x+h)-f(x))/h and have gotten it down to (h+radical(x+h)-radical(x))/h but Im stuck now... Whats my next step?
... conjugate ...

10-05-2009, 12:47 AM   #142
3kingme3
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by thylacine ... conjugate ...
do you mean turn it to h+(x+h)^1/2 -(x)^1/2 all over h, because if so I still dont know what to do next, and if not I dont remember what conjugating is

10-05-2009, 02:19 AM   #143
3kingme3
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by 3kingme3 do you mean turn it to h+(x+h)^1/2 -(x)^1/2 all over h, because if so I still dont know what to do next, and if not I dont remember what conjugating is
I got it thanks anyway guys, Im sure ill be back

 10-05-2009, 04:02 PM #144 smcdonn2 centurion   Join Date: Jul 2009 Posts: 165 Re: The Official Math/Physics/Whatever Homework questions thread Im stuck on a couple probability questions Suppose X is a binomial random variable with n=10 and p=2/5. What is the expected valueof 3X-4?
 10-05-2009, 04:04 PM #145 smcdonn2 centurion   Join Date: Jul 2009 Posts: 165 Re: The Official Math/Physics/Whatever Homework questions thread Probability let X have the pdf fx(x) = {2(1-x), 0<= x <=1 or 0, elsewhere} Suppose that Y=g(x)=X^3 find E(Y) two different ways
 10-07-2009, 12:04 PM #146 smcdonn2 centurion   Join Date: Jul 2009 Posts: 165 Re: The Official Math/Physics/Whatever Homework questions thread Lets H be a subgroup of a group G such that g^-1hg is an element of H for all g element of G and all h is an element of H. show that every left coset gH is the same as every right coset Hg.
10-07-2009, 01:36 PM   #147
lastcardcharlie
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by smcdonn2 Lets H be a subgroup of a group G such that g^-1hg is an element of H for all g element of G and all h is an element of H. show that every left coset gH is the same as every right coset Hg.
Use x = hg <-> h' = g^-1hg = g^-1x <-> x = gg^-1x = gh'.

10-07-2009, 02:30 PM   #148
RosieTheGreat
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by smcdonn2 Lets H be a subgroup of a group G such that g^-1hg is an element of H for all g element of G and all h is an element of H. show that every left coset gH is the same as every right coset Hg.
Last cardcharlie got it right, but remember this theorem as it will become very important.

 10-07-2009, 03:07 PM #149 solsek Carpal \'Tunnel     Join Date: Feb 2008 Posts: 6,003 Re: The Official Math/Physics/Whatever Homework questions thread Probably a really easy question, but how do you solve |1 + i | = ?. And converting re^itheta to a + bi and from a + bi to re^itheta?
10-07-2009, 03:26 PM   #150
lastcardcharlie
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by solsek Probably a really easy question, but how do you solve |1 + i | = ?. And converting re^itheta to a + bi and from a + bi to re^itheta?
|a + bi| = sqrt(a^2 + b^2) = r and b/a = tan(theta).

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