Lecture Notes Example 3.7c.pdf - (c Let p = P(Head We first calculate P(HHH = p3 P(HHT = p2(1 p 2 p P(HTT = p(1 p)2 P(THH =(1 p)p2 P(THT = p(1 p)2 P(HTH

# Lecture Notes Example 3.7c.pdf - (c Let p = P(Head We first...

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(c) Let p = P ( Head ) . We first calculate P ( HHH ) = p 3 P ( HHT ) = p 2 ( 1 - p ) P ( HTH ) = p 2 ( 1 - p ) P ( HTT ) = p ( 1 - p ) 2 P ( THH ) = ( 1 - p ) p 2 P ( THT ) = p ( 1 - p ) 2 P ( TTH ) = p ( 1 - p ) 2 P ( TTT ) = ( 1 - p ) 3 Now, f ( 0 ) = P ( TTT ) = ( 1 - p ) 3 f ( 1 ) = P ( HTT , THT , TTH ) = 3 p ( 1 - p ) 2 f ( 2 ) = P ( HHT , HTH , THH ) = 3 p 2 ( 1 - p ) f ( 3 ) = P ( HHH ) = p 3 So, the PMF of

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