Whats the most insightful probability post ever posted on here?
it would be interesting to see....
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Re: Whats the most insightful probability post ever posted on here?
I really liked BruceZ's inclusion-exlusion post... It might not be the most insightful, but I hope that by mentioning it he'll appear like a magic genie and post a link [img]/images/graemlins/smile.gif[/img] (I'm too lazy to search, and too lazy to PM him, so I guess if I never see the post again it'll be my own damn fault)
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Re: Whats the most insightful probability post ever posted on here?
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I really liked BruceZ's inclusion-exlusion post... It might not be the most insightful, but I hope that by mentioning it he'll appear like a magic genie and post a link [img]/images/graemlins/smile.gif[/img] (I'm too lazy to search, and too lazy to PM him, so I guess if I never see the post again it'll be my own damn fault) [/ QUOTE ] The second most beautiful counting method in combinatorics: Inclusion-Exclusion |
Re: Whats the most insightful probability post ever posted on here?
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The second most beautiful counting method in combinatorics: Inclusion-Exclusion [/ QUOTE ] The first being? |
Re: Whats the most insightful probability post ever posted on here?
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[ QUOTE ] I really liked BruceZ's inclusion-exlusion post... It might not be the most insightful, but I hope that by mentioning it he'll appear like a magic genie and post a link [img]/images/graemlins/smile.gif[/img] (I'm too lazy to search, and too lazy to PM him, so I guess if I never see the post again it'll be my own damn fault) [/ QUOTE ] The second most beautiful counting method in combinatorics: Inclusion-Exclusion [/ QUOTE ] Awesome dude, thanks! |
Re: Whats the most insightful probability post ever posted on here?
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[ QUOTE ] The second most beautiful counting method in combinatorics: Inclusion-Exclusion [/ QUOTE ] The first being? [/ QUOTE ] The method of double counting. |
Re: Whats the most insightful probability post ever posted on here?
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[ QUOTE ] [ QUOTE ] The second most beautiful counting method in combinatorics: Inclusion-Exclusion [/ QUOTE ] The first being? [/ QUOTE ] The method of double counting. [/ QUOTE ] What's the difference? |
Re: Whats the most insightful probability post ever posted on here?
You lost me. Could we maybe have a link or thread for that too? Thanks!
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Re: Whats the most insightful probability post ever posted on here?
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[ QUOTE ] [ QUOTE ] [ QUOTE ] The second most beautiful counting method in combinatorics: Inclusion-Exclusion [/ QUOTE ] The first being? [/ QUOTE ] The method of double counting. [/ QUOTE ] What's the difference? [/ QUOTE ] Double counting means enumerating a set by counting the objects in the set in two different ways and then equating them to arrive at the answer. Inclusion-exclusion is the method of enumerating a set by overcounting and undercounting repeatedly to arrive at the answer. |
Re: Whats the most insightful probability post ever posted on here?
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[ QUOTE ] [ QUOTE ] [ QUOTE ] [ QUOTE ] The second most beautiful counting method in combinatorics: Inclusion-Exclusion [/ QUOTE ] The first being? [/ QUOTE ] The method of double counting. [/ QUOTE ] What's the difference? [/ QUOTE ] Double counting means enumerating a set by counting the objects in the set in two different ways and then equating them to arrive at the answer. [/ QUOTE ] Example: Compute the sum S = 1 + 2 + 3 + ... + 100. S = 100 + 99 + 98 + ... + 1 Adding the above two equations gives: 2S = 101 + 101 + 101 + ...(100 times) 2S = 101*100 = 10,100 S = 5,050 Example: Compute the sum S = 1 + 1/2 + 1/4 + 1/8 + ... (1/2)*S = 1/2 + 1/4 + 1/8 + ... Subtracting these gives: (1/2)*S = 1 S = 2. Example: S = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ... S = 1 + 1/S S^2 = S + 1 = 0 S^2 - S - 1 = 0 S = 1/2 + sqrt(5)/2 Example: S = sqrt(1 + sqrt(1 + sqrt(1 + sqrt(1 + ... S = sqrt(1 + S) S^2 = 1 + S S^2 - S - 1 = 0 S = 1/2 + sqrt(5)/2 A well-known mathematician once told me that there are 4 tricks used to derive everything in applied mathematics (or something like that): 1. Exchange the order of integration or summation. 2. Integrate by parts. 3. Add and subtract 1. 4. Induction. |
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