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A gambler repeatedly bets that a die will come up 6 when

Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp ISBN: 9780495391326 48

Solution for problem 23E Chapter 9.8

Discrete Mathematics with Applications | 4th Edition

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Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp

Discrete Mathematics with Applications | 4th Edition

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Problem 23E

A gambler repeatedly bets that a die will come up 6 when rolled. Each time the die comes up 6, the gambler wins $1; each time it does not, the gambler loses $1. He will quit playing either when he is ruined or when he wins $300. If Pn is the probability that the gambler is ruined when he begins play with $n, then  for all integers k with 2 ≤ k ≤ 300. Also P0 = 1 and P300 = 0. Find an explicit formula for Pn and use it to calculate P20. (Exercise 33 in Section 9.9 asks you to derive the recurrence relation.)

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Advertising Test 3 Study Guide: Key Terms: Chapter 12: Media Planning Essentials • Deal proneness: the ease with which a consumer can get a deal, know what a good deal is, operate with knowledge of what a good price would be, and know a seller’s cost • Price/cost transparency: ease with which consumers can find out the price of a product and the seller’s cost • Above-the-line promotion: traditional measured media advertising; any message broadcast to the public through conventional means such as TV, internet, radio, and magazines • Measured media: media that are closely measured to determine advertising costs and effectiveness; TV, radio, newspaper, magazines and outdoor media • Below-the-line promotion: a promotional effort that includes in-store promotions, coupons, dealer discounts, and product placement • Unmeasured media: Media less formally measured for advertising costs and effectiveness direct mail, catalogs, special events, and other ways to reach business and household consumers • Media plan: specifies the media in which advertising messages will be places to reach the desired audience • Media class: broad category of media, such as TV, radio, or newspapers • Media vehicle: a particular option for placement within a medial class; example Newsweek is a media vehicle within the magazine-media class • Media mix: the blend of different media that will be used to effectively reach the target audience • Single-source marketing service: research service that offer information not only on demographics, but also on brands, purchase frequency, prices paid, and media exposure; example BehaviorScan • Geographic scope: scope of the geographic area to be covered by advertising media • Geo-targeting: the placement of ads in geographic regions where higher purchase tendencies for a brand are evident • Reach: the number of people or households in a target audience that will be exposed to a media vehicle or schedule at least one time during a given period of time; often expressed as a percentage • Frequency: the average number of times an individual or household within a target audience is exposed to a media vehicle in a given period of time (typically a week or a month) • Effective frequency: the number of times a target audience needs to be exposed to a message before the objective of the advertisers are met- either communication objectives or sales impact • Effective reach: the number or percentage of consumers in the target audience that are exposed to an ad some minimum number of times • Message weight: the total mass of advertising delivered • Gross impressions: the sum of exposures to the entire media placement in a media plan; 2 types – potential ad impressions/opportunities (program or publication) and message impressions (exposure to ads themselves) • Between-vehicle duplication: exposure to the same advertisement in different media • Within-vehicle duplication: exposure to the same advertisement in the same media at different times • Continuity: the pattern of placement of advertisements in a media schedule • Continuous scheduling: a patter of placing ads at a steady rate over a period of time • Flighting: media scheduling strategy achieved by scheduling heavy advertising for a period of time, usually two weeks, then stopping advertising altogether for a period, only to come back with another heavy schedule • Pulsing: media scheduling strategy that combines elements from continuous and flighting techniques; advertisements are scheduled continuously in media over a period of time, but with periods or much heavier scheduling; appropriate for products sold year long but with seasonal requirements (i.e. clothing) • Forgetting function: idea that people’s forgetting is fairly predictable and seems to obey a mathematical function • Square root law: the recognition of print ads increases with the square of the illustration (size) • Context effects: how the context of the media through which an ad is presented affects consumers’ impression of the ad • Share of voice: the calculation of any one of advertiser’s brand expenditures relative to the overall spending in a category o Share of Voice = 1 brand’s advertising expenditures in a medium/ Total product category ad expenditures in a medium • Cost per thousand (CPM): the dollar cost of reaching the 1000 members of an audience using a particular medium • Cost per thousand-target market (CPM-TM): cost of media buy/targeted audience x 1000 • Cost per rating point (CPRP): $ for a program placement/program rating o CPRP = dollar cost of ad placement on a program/ Program rating • RSS (Really Simple Syndication): a channel or feed from blogs, podcasts, or other content that the computer user has linked to • Net promoter scores: essential good mentions-bad mentions • Media buying: securing the electronic media time and print media space specified in the schedule • Agency of record: the advertising agency chosen by the advertiser to purchase time and space • Upfronts: a period where the TV networks reveal their fall line-ups and pre-sell advertising on them • Media-buying service: an independent organization that specializes in buying large blocks of media time and space and reselling it to advertisers Chapter 13: Media Planning: Newspapers, Magazines, TV, and Radio Newspapers • Display advertising: newspapers; standard components used to set ad off from the news content • Co-op advertising: manufacturer pays part of the media bill when a merchant features the manufacturer’s brand in advertising • Preprinted insert: an ad delivered to the newspaper fully printed and ready for insertion into the newspaper • Free-standing inserts (FSI): coupons • Classified advertising: newspaper ads that appear as all copy messages under categories such as employment and auto • Rate card: contains info on costs, closing times, specifications, and special pages or features available in the newspaper • Column inch: unit of space 1in. deep by 1 column wide • Standard advertising unit (SAU): system for selling ad spaces • Run-of-paper (ROP): ad may appear anywhere, on any page in paper • Preferred position: ad placed in specific section • Full position: ad placed near the top of page or in the middle of editorial material • Circulation: the number of newspapers distributed each day • Paid circulation: the number of copies sold through subscriptions and newsstand distribution • Controlled circulation: the number of copies of the newspaper that are given away free • Readership: the measure of the circulation multiplied by the number of readers of a copy • Hyper-localism: provide in-depth coverage of local issues • Pay-for-inquiry advertising model: a payment scheme in which the medium gets paid by advertisers based solely on the inquiries an advertiser receives in response to an ad Magazines • Bleed page: background color runs to end of page • Gatefold ads: ads that fold out of a magazine • First cover page: front cover • Second cover page: inside front cover • Third cover page: inside back cover • Furth cover page: back cover • Double-page spreads: ads that bridge two facing pages • Space contract: establishes a rate for all ads placed in a publication • Space order: insertion order; commitment by an advertisers to ad space in a particular issue • Closing date: the date when production ready ad materials must be delivered • On-sale date: date magazine is issued to subscribers/sold in stores • Cover date: date of publication that appears on magazine • Guaranteed circulation: a stated minimum number of copies of an issue • Pass-along readership: additional number of people, other than readers who may see publication Television • Cable TV • Video on demand (VOD) • Off-network syndication: programs that were previously run in network prime time • First-sun syndication: programs developed specifically for sale to individual stations • Barter syndication: both off-network and first-run syndication shows offered free or at a reduced rate to local television stations • Satellite and closed-circuit • Narrowcasting: the development and delivery of specialized programming to well- defined audiences • Channel grazing: using a remote control to monitor programming on other channels while an ad is being played; avoid ad • V-chip: a device that can block TV programming based on rating • Digital video recorders (DVR) sponsorship: advertiser agrees to pay for the production of a TV program and for most of the ads that appear in the program • Participation: several different advertisers by commercial time during a specific TV program • Spot advertising: all TV ad time purchased from and aired through local TV stations • Dayparts: TV program times • TV Households: households that own...

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Chapter 9.8, Problem 23E is Solved
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Textbook: Discrete Mathematics with Applications
Edition: 4
Author: Susanna S. Epp
ISBN: 9780495391326

The full step-by-step solution to problem: 23E from chapter: 9.8 was answered by , our top Math solution expert on 07/19/17, 06:34AM. This full solution covers the following key subjects: gambler, wins, ruined, die, integers. This expansive textbook survival guide covers 131 chapters, and 5076 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics with Applications , edition: 4. Since the solution to 23E from 9.8 chapter was answered, more than 246 students have viewed the full step-by-step answer. The answer to “A gambler repeatedly bets that a die will come up 6 when rolled. Each time the die comes up 6, the gambler wins $1; each time it does not, the gambler loses $1. He will quit playing either when he is ruined or when he wins $300. If Pn is the probability that the gambler is ruined when he begins play with $n, then for all integers k with 2 ? k ? 300. Also P0 = 1 and P300 = 0. Find an explicit formula for Pn and use it to calculate P20. (Exercise 33 in Section 9.9 asks you to derive the recurrence relation.)” is broken down into a number of easy to follow steps, and 106 words. Discrete Mathematics with Applications was written by and is associated to the ISBN: 9780495391326.

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A gambler repeatedly bets that a die will come up 6 when