Pr{A = k} otherwise andom sequence {X;}, as: А, li>1: if X; = 1 Xi+1 if X; = 2 Xi+1 if X; = 3 Xi+1 }, Markov? e the random sequence {Y;} according to: 1 if X; = 1 2 otherwise Y; = that {Y;}, is not Markov.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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9. Let A be a random variable with the following distribution:
for k = 1,2,3
Pr {A = k} =
otherwise
Define a random sequence {X;} as:
• X1 = A,
• for all i> 1:
if X; = 1
X;+1 =2
if X; = 2
X;+1 =3
%3D
if X; = 3
Xi+1 =1
%3D
(a) Is {X;}, Markov?
(b) Define the random sequence {Y;}, according to:
S1 if X; = 1
Y; =
2 otherwise
Show that {Y:} is not Markov.
介 介 介
Transcribed Image Text:9. Let A be a random variable with the following distribution: for k = 1,2,3 Pr {A = k} = otherwise Define a random sequence {X;} as: • X1 = A, • for all i> 1: if X; = 1 X;+1 =2 if X; = 2 X;+1 =3 %3D if X; = 3 Xi+1 =1 %3D (a) Is {X;}, Markov? (b) Define the random sequence {Y;}, according to: S1 if X; = 1 Y; = 2 otherwise Show that {Y:} is not Markov. 介 介 介
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