8. Consider a simple random walk starting at 0 in which each step is to the right with probability p (= 1 – q). Let T, be the number of steps until the walk first reaches b where b > 0. Show that E(T, | Tħ < ∞) =b/\p – ql.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 64E
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Consider a simple random walk starting at 0 in which each step is to the right with probability
p (= 1 – q). Let T, be the number of steps until the walk first reaches b where b > 0. Show that
E(T, | Th < ∞) = b/\p – ql.
8.
Transcribed Image Text:Consider a simple random walk starting at 0 in which each step is to the right with probability p (= 1 – q). Let T, be the number of steps until the walk first reaches b where b > 0. Show that E(T, | Th < ∞) = b/\p – ql. 8.
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