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# Kelly makes a series of n bets, each of which she has probability p of winning

ISBN: 9781466575578 423

## Solution for problem 24 Chapter 9

Introduction to Probability | 1st Edition

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Problem 24

Kelly makes a series of n bets, each of which she has probability p of winning, independently. Initially, she has x0 dollars. Let Xj be the amount she has immediately after her jth bet is settled. Let f be a constant in (0, 1), called the betting fraction. On each bet, Kelly wagers a fraction f of her wealth, and then she either wins or loses that amount. For example, if her current wealth is \$100 and f = 0.25, then she bets \$25 and either gains or loses that amount. (A famous choice when p > 1/2 is f = 2p 1, which is known as the Kelly criterion.) Find E(Xn) (in terms of n, p, f, x0). Hint: First find E(Xj+1|Xj )

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Statistics: Intro information  Data: What is it o information we collect and organize o facts and figures o numbers and text  What is the point of Statistics o To process data so that it is useful o Provide meaningful information in an easily accessible way o Answer questions o Tell a story  Help business leaders o Improved insight about operations o Make decisions that are: (prove your opinion is right)  Data-driven  Fact-based o Not based on speculation o EX: UPS, to increase productivity  Benefits of Data and Statistics o Reduce cost o Increase profit

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##### ISBN: 9781466575578

This full solution covers the following key subjects: . This expansive textbook survival guide covers 13 chapters, and 602 solutions. This textbook survival guide was created for the textbook: Introduction to Probability, edition: 1. The answer to “Kelly makes a series of n bets, each of which she has probability p of winning, independently. Initially, she has x0 dollars. Let Xj be the amount she has immediately after her jth bet is settled. Let f be a constant in (0, 1), called the betting fraction. On each bet, Kelly wagers a fraction f of her wealth, and then she either wins or loses that amount. For example, if her current wealth is \$100 and f = 0.25, then she bets \$25 and either gains or loses that amount. (A famous choice when p > 1/2 is f = 2p 1, which is known as the Kelly criterion.) Find E(Xn) (in terms of n, p, f, x0). Hint: First find E(Xj+1|Xj )” is broken down into a number of easy to follow steps, and 124 words. Introduction to Probability was written by and is associated to the ISBN: 9781466575578. The full step-by-step solution to problem: 24 from chapter: 9 was answered by , our top Statistics solution expert on 03/14/18, 07:48PM. Since the solution to 24 from 9 chapter was answered, more than 249 students have viewed the full step-by-step answer.

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