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dc.contributor.authorDrekic, Steve
dc.contributor.authorSpivey, Michael Z. 14:35:36 (GMT) 14:35:36 (GMT)
dc.descriptionThe final publication is available at Elsevier via© (2021). This manuscript version is made available under the CC-BY-NC-ND 4.0 license
dc.description.abstractA sequence of independent Bernoulli trials, each of which is a success with probability p, is conducted. For k ∈ Z+, let Xk be the number of trials required to obtain k consecutive successes. Using techniques from elementary probability theory, we present a derivation which ultimately yields an elegant expression for the probability mass function of Xk, and is simpler in comparison to what is found in the literature. Following this, we use our derived formula to obtain explicit closed-form expressions for the complementary cumulative distribution function and the nth factorial moment of Xk.en
dc.description.sponsorshipFunder 1, Natural Sciences and Engineering Research Council of Canada through its Discovery Grants program (RGPIN-2016-03685).en
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.subjectBernoulli trialsen
dc.subjectConsecutive successesen
dc.subjectFactorial momentsen
dc.subjectGenerating functionen
dc.subjectPolynomial coefficientsen
dc.subjectBell polynomialsen
dc.titleOn the Number of Trials Needed to Obtain k Consecutive Successesen
dcterms.bibliographicCitationDrekic, S., & Spivey, M. Z. (2021). On the number of trials needed to obtain k consecutive successes. Statistics & Probability Letters, 176, 109132.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Statistics and Actuarial Scienceen

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