For this probability question, a coin with probability p of heads is flipped until both heads and tails appears. For finding the Expectation of the number of flips, I do not understand how E[X | first head] = (1 + 1/(1+p)) and the same for the tails first.
For this probability question, a coin with probability p of heads is flipped until both heads and tails appears. For finding the Expectation of the number of flips, I do not understand how E[X | first head] = (1 + 1/(1+p)) and the same for the tails first.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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For this probability question, a coin with probability p of heads is flipped until both heads and tails appears. For finding the Expectation of the number of flips, I do not understand how E[X | first head] = (1 + 1/(1+p)) and the same for the tails first.
![E [X] = E [X|first head] P [first head] + E [X|first tail] P [first tail]
E [X] =
(1
(1+)p+ (1+) (1-P)
p)
p²+(1-p)²
(1 + P²HLL-D² )
p(1+p)
E [X] = (1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090581ae-a74e-4a4a-a813-d3475fc39629%2F38827cc1-4142-4b1c-9749-41989e120ab7%2F8dzm726_processed.png&w=3840&q=75)
Transcribed Image Text:E [X] = E [X|first head] P [first head] + E [X|first tail] P [first tail]
E [X] =
(1
(1+)p+ (1+) (1-P)
p)
p²+(1-p)²
(1 + P²HLL-D² )
p(1+p)
E [X] = (1
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