A fair coin is tossed successively. Let X; = +1 if the jth toss is a head, -1 if the jth toss is a tail. Define the difference between the number of heads +Xj. Show that the probability that the and X; and tails after j tosses by S; = X1+X2+ last time there was an equal number of heads and tails within 2n tosses occurred at the 2kth toss is Pr{S2k = 0} · Pr{S2n–2k = 0}. ...
A fair coin is tossed successively. Let X; = +1 if the jth toss is a head, -1 if the jth toss is a tail. Define the difference between the number of heads +Xj. Show that the probability that the and X; and tails after j tosses by S; = X1+X2+ last time there was an equal number of heads and tails within 2n tosses occurred at the 2kth toss is Pr{S2k = 0} · Pr{S2n–2k = 0}. ...
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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
Transcribed Image Text:A fair coin is tossed successively. Let X; = +1 if the jth toss is a head,
and X; = -1 if the jth toss is a tail. Define the difference between the number of heads
and tails after j tosses by S; = X1+X2+
last time there was an equal number of heads and tails within 2n tosses occurred at
the 2kth toss is Pr{S2k = 0} · Pr{S2n-2k = 0}.
+Xj. Show that the probability that the
...
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