What Does Not Exhaustive Mean Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers
Independent event the occurrence of one event does not affect the occurrence of the others e g if we flip a coin two times the first time may show a head but this does not guarantee that the next time when we flip the coin the outcome will also be heads From this example we can see the first event does not affect the occurrence of the next Possible results are mutually exclusive and exhaustive Hypotheses unlike results are neither mutually exclusive nor exhaustive Is it true that possible results are exhaustive For example if we consider a continuum density probability there is an infinite number of possible results so aren t we non exhaustive
What Does Not Exhaustive Mean
What Does Not Exhaustive Mean
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In some but not all texts mutually exclusive is a slightly different property of events sets in a probability space Two events are mutually exclusive if the probability of them both occurring is zero that is if operatorname Pr A cap B 0 With that definition disjoint sets are necessarily mutually exclusive but mutually EXHAUSTIVE PROOF Some theorems can be proved by examining a relatively small number of examples Such proofs are called exhaustive proofs or proofs by exhaustion because these proofs proceed by exhausting all possibilities An exhaustive proof is a special type of proof by cases where each case involves checking a single example
begingroup Someone else posted this same question today and then deleted it The question had some phrasing that prompted me to write this comment which is may be relevant here but when I tried to save the comment the question had been deleted It doesn t mean thorough or exhaustive although those may be consequences Just to make sure what I mean by collectively exhaustive cases is that they are cases such at at least one of them must occur For instance the cases 1 my calculator is in my bag and 2 my calculator is not in my bag are collectively exhaustive one of them must be true there is absolutely no other option
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Two or more events are collectively exhaustive if they cover entire sample space Two or more events are independent if occurance or failure of one does not affect occurance or failure of other Are these definitions correct Is it possible that a given set of events is collectively exhaustive amd independent at the same time begingroup Jus to add mutual independence as seen above is a harder claim and implies pairwise indolence but it is not so the other way round endgroup jia chen Commented Feb 2 2020 at 11 25
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Independent event the occurrence of one event does not affect the occurrence of the others e g if we flip a coin two times the first time may show a head but this does not guarantee that the next time when we flip the coin the outcome will also be heads From this example we can see the first event does not affect the occurrence of the next
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What Does Not Exhaustive Mean - Just to make sure what I mean by collectively exhaustive cases is that they are cases such at at least one of them must occur For instance the cases 1 my calculator is in my bag and 2 my calculator is not in my bag are collectively exhaustive one of them must be true there is absolutely no other option
