I toss a coin which lands heads with probability p. Let WH be the number of tosses till I get a head, WHH the number of tosses till I get two heads in a row, and WHHH the number of tosses till I get three heads in a row. Find: a) E(WH); b) E(WHH) [Hint: condition on whether the first toss was heads or

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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I toss a coin which lands heads with probability p. Let WH be the number of tosses till
I get a head, WHh the number of tosses till I get two heads in a row, and WHHH the
number of tosses till I get three heads in a row. Find:
a) E(WH); b) E(WHH) (Hint: condition on whether the first toss was heads or
tails); c) E(WHHH) [Hint: condition on WT).
d) Generalize to find the expected number of tosses to obtain m heads in a row.
Transcribed Image Text:I toss a coin which lands heads with probability p. Let WH be the number of tosses till I get a head, WHh the number of tosses till I get two heads in a row, and WHHH the number of tosses till I get three heads in a row. Find: a) E(WH); b) E(WHH) (Hint: condition on whether the first toss was heads or tails); c) E(WHHH) [Hint: condition on WT). d) Generalize to find the expected number of tosses to obtain m heads in a row.
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