Miscellaneous Topics

Melvin Hausner
Additional contact information
Melvin Hausner: New York University, Washington Square and University College

Chapter Chapter 4 in Elementary Probability Theory, 1995, pp 123-151 from Springer

Abstract: Abstract Suppose that an experiment has probability space S, and that A is an event of S with probability p = p(A). We let P n denote the probability that the event A will occur at least once if the experiment is repeated, independently, for n times. By Theorem 37 of Chapter 3, we have 4.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa % aaleaacaWGUbaabeaakiabg2da9iaaigdacqGHsislcaGGOaGaaGym % aiabgkHiTiaadchacaGGPaWaaWbaaSqabeaacaWGUbaaaaaa!3FB6! $$ {P_n} = 1 - {(1 - p)^n} $$ The cases p = 0 and p = 1 naturally give P n = 0 and P n = 1, while the case n = 1 naturally gives P 1 = p. We shall therefore usually assume that n > 1 and 4.2 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGimaiabgY % da8iaadchacqGH8aapcaaIXaaaaa!3A66! $$ 0

Keywords: Sample Point; Random Walk; Sample Space; Infinite Series; Uniform Space (search for similar items in EconPapers)
Date: 1995
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-1753-5_4

Ordering information: This item can be ordered from
http://www.springer.com/9781461517535

DOI: 10.1007/978-1-4615-1753-5_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().