Matches in SemOpenAlex for { <https://semopenalex.org/work/W2510432717> ?p ?o ?g. }
Showing items 1 to 54 of
54
with 100 items per page.
- W2510432717 endingPage "5710" @default.
- W2510432717 startingPage "5693" @default.
- W2510432717 abstract "A classical probability question asks for the expected waiting time for flipping a coin (fair or not) until a series of consecutive k heads occur. Now instead of k heads, we can ask for the expected waiting time for a prescribed string such as HTHHTT (H for ‘head’ and T for ‘tail’), and furthermore, the following more general setting: replacing coin flipping by taking a letter, one at a time, what is the expected waiting time until a prescribed string (a series of letters) is reached? Here we allow different probabilities for the occurrence of different letters. We give an exposition to this problem by offering an elementary algorithm and implementing it to compute the corresponding probability generating function: we show that there exists a universal program taking as inputs the choice of letters with given probabilities and the prescribed string, and as output, returning the probability generating function for the waiting time. The same method is applied to solve the problem of several competing strings, which asks for the probability (or more generally the probability generating function) of one of the given strings occurring before the remaining strings. In particular, this solves the problem of finding the expectation and variance for the waiting time random variable of the first problem." @default.
- W2510432717 created "2016-09-16" @default.
- W2510432717 creator A5022822554 @default.
- W2510432717 creator A5032412405 @default.
- W2510432717 creator A5067761799 @default.
- W2510432717 date "2013-01-01" @default.
- W2510432717 modified "2023-09-25" @default.
- W2510432717 title "Computing probability generating functions of coin flipping and its generalizations" @default.
- W2510432717 cites W104215891 @default.
- W2510432717 cites W1484657710 @default.
- W2510432717 cites W1511368807 @default.
- W2510432717 cites W1536639614 @default.
- W2510432717 cites W1982046147 @default.
- W2510432717 cites W2038994416 @default.
- W2510432717 cites W2068112586 @default.
- W2510432717 cites W2074882352 @default.
- W2510432717 cites W2119478675 @default.
- W2510432717 cites W2156024151 @default.
- W2510432717 cites W2562347433 @default.
- W2510432717 cites W2751862591 @default.
- W2510432717 doi "https://doi.org/10.12988/ams.2013.38460" @default.
- W2510432717 hasPublicationYear "2013" @default.
- W2510432717 type Work @default.
- W2510432717 sameAs 2510432717 @default.
- W2510432717 citedByCount "1" @default.
- W2510432717 countsByYear W25104327172021 @default.
- W2510432717 crossrefType "journal-article" @default.
- W2510432717 hasAuthorship W2510432717A5022822554 @default.
- W2510432717 hasAuthorship W2510432717A5032412405 @default.
- W2510432717 hasAuthorship W2510432717A5067761799 @default.
- W2510432717 hasConcept C33923547 @default.
- W2510432717 hasConcept C41008148 @default.
- W2510432717 hasConceptScore W2510432717C33923547 @default.
- W2510432717 hasConceptScore W2510432717C41008148 @default.
- W2510432717 hasLocation W25104327171 @default.
- W2510432717 hasOpenAccess W2510432717 @default.
- W2510432717 hasPrimaryLocation W25104327171 @default.
- W2510432717 hasRelatedWork W1974891317 @default.
- W2510432717 hasRelatedWork W1979597421 @default.
- W2510432717 hasRelatedWork W2007980826 @default.
- W2510432717 hasRelatedWork W2061531152 @default.
- W2510432717 hasRelatedWork W2069964982 @default.
- W2510432717 hasRelatedWork W2313400459 @default.
- W2510432717 hasRelatedWork W2748952813 @default.
- W2510432717 hasRelatedWork W2899084033 @default.
- W2510432717 hasRelatedWork W4225152035 @default.
- W2510432717 hasRelatedWork W4245490552 @default.
- W2510432717 hasVolume "7" @default.
- W2510432717 isParatext "false" @default.
- W2510432717 isRetracted "false" @default.
- W2510432717 magId "2510432717" @default.
- W2510432717 workType "article" @default.