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

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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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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