1 ( iii ) Explain why �1
� . 2
( iv ) Write down �2: �3: �
4.
[ 7 ]
�0� � � 0
( e ) Show that the steady state probability vector is v � � �. � 0 � � � �1�
[ 4 ]
Now , the fair coin used in the game is replaced by another biased coin such 1 that p � . 3
( f ) Find the probability that a player tosses the coin for
( i ) five times to get the first three consecutive heads ;
( ii ) seven times to get the first three consecutive heads ;
( iii ) at least eight times . [ 10 ]
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