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Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Con sider a fandom walk on the Integers. That is, let there be a Player A who wins $1 each time a Vandom Coin Comes up head and loses $1 each time it Comes up tail, A Starts with o dlollers. Assume that the Coin tosses arre in depen dent and that each timi head Occurs with Pro bability P, with Y2 <P< 1. Consider the following random Variables :
Transcribed Image Text:Con sider a fandom walk on the Integers. That is, let there be a Player A who wins $1 each time a Vandom Coin Comes up head and loses $1 each time it Comes up tail, A Starts with o dlollers. Assume that the Coin tosses arre in depen dent and that each timi head Occurs with Pro bability P, with Y2 <P< 1. Consider the following random Variables :
Wa is the nember of steps until A has $1.for time. We is the neumber of Steps until A bes $2 for the first time. Wg is the nember of steps Until A has $ 3 for the fint timt. Xx = Wy-Wt Xg= Wg -Wz Since Prob(U,{W = i}) =1 we reatriet the Sample space to Consist of finite Seguence of Coin tosses, Assume that the Sample Space Consists g this Countably finite set. A) Which three of these Pamdom Variablos are lutully Indygandat BFO each Pair of Random Variables that are not indepen dent, Show that they are ust Indepentent C) Give the expected Value of each of these romdom Varlables · DLWas it important for your answer that ½ ?p<1? what thappem if P=I?
Transcribed Image Text:Wa is the nember of steps until A has $1.for time. We is the neumber of Steps until A bes $2 for the first time. Wg is the nember of steps Until A has $ 3 for the fint timt. Xx = Wy-Wt Xg= Wg -Wz Since Prob(U,{W = i}) =1 we reatriet the Sample space to Consist of finite Seguence of Coin tosses, Assume that the Sample Space Consists g this Countably finite set. A) Which three of these Pamdom Variablos are lutully Indygandat BFO each Pair of Random Variables that are not indepen dent, Show that they are ust Indepentent C) Give the expected Value of each of these romdom Varlables · DLWas it important for your answer that ½ ?p<1? what thappem if P=I?
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