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An arcade machine costs one dollar to play. Every time you play, there is a 1/10 chance of winning.(a) Let A be the number of times you play until you win. Find the variance Var[A].(b) Ten people play the arcade machine; each one keeps playing until they win, and thenit’s the next person’s turn. Let B be the number of times they play in total. Find thevariance Var[B].(c) Ten years later, you come back to the arcade machine, and it’s exactly the same, exceptthat due to inflation, the machine costs $10 to play.Let C be the the total cost of playing until you win. Find the variance Var[C].

An arcade machine costs one dollar to play. Every time you play, there is a 1/10 chance of winning.(a) Let A be the number of times you play until you win. Find the variance Var[A].(b) Ten people play the arcade machine; each one keeps playing until they win, and thenit’s the next person’s turn. Let B be the number of times they play in total. Find thevariance Var[B].(c) Ten years later, you come back to the arcade machine, and it’s exactly the same, exceptthat due to inflation, the machine costs $10 to play.Let C be the the total cost of playing until you win. Find the variance Var[C].

A First Course in Probability (10th Edition)
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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An arcade machine costs one dollar to play. Every time you play, there is a 1/10 chance of winning.
(a) Let A be the number of times you play until you win. Find the variance Var[A].
(b) Ten people play the arcade machine; each one keeps playing until they win, and then
it’s the next person’s turn. Let B be the number of times they play in total. Find the
variance Var[B].
(c) Ten years later, you come back to the arcade machine, and it’s exactly the same, except
that due to inflation, the machine costs $10 to play.
Let C be the the total cost of playing until you win. Find the variance Var[C].

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