public:calculating_the_size_of_a_set_by_observing_the_proportionality_change_of_its_disjoint_subsets
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public:calculating_the_size_of_a_set_by_observing_the_proportionality_change_of_its_disjoint_subsets [2019/04/16 11:02] – [Background] fangfufu | public:calculating_the_size_of_a_set_by_observing_the_proportionality_change_of_its_disjoint_subsets [2019/04/17 02:08] (current) – [Formal Problem statement] fangfufu | ||
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We can consider everyone who voted in an Instagram poll as a set, and the two options are disjoint subsets of the superset. | We can consider everyone who voted in an Instagram poll as a set, and the two options are disjoint subsets of the superset. | ||
- | ===== Formal | + | ===== Formal |
Set $A$ consists of disjoint subsets $a_1, a_2, ..., a_n$. Although we do not know the cardinality of set $A$ (denoted by $|A|$) and the cardinality of each of the subset, we do know the proportion of each subset in terms of set $A$, that is we know $\frac{|a_1|}{|A|}, | Set $A$ consists of disjoint subsets $a_1, a_2, ..., a_n$. Although we do not know the cardinality of set $A$ (denoted by $|A|$) and the cardinality of each of the subset, we do know the proportion of each subset in terms of set $A$, that is we know $\frac{|a_1|}{|A|}, | ||
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By dividing the above equation by $|A|$ and rearrangement, | By dividing the above equation by $|A|$ and rearrangement, | ||
- | $$ |A| = \frac{-n(\delta_{a_1} | + | $$ |A| = \frac{n(1 - \alpha_1 - \delta_{a_1})}{\delta_{a_1}} $$ |
You know everything in the right hand side of the equation, so solving $|A|$ is very easy. | You know everything in the right hand side of the equation, so solving $|A|$ is very easy. | ||
public/calculating_the_size_of_a_set_by_observing_the_proportionality_change_of_its_disjoint_subsets.txt · Last modified: 2019/04/17 02:08 by fangfufu