6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5 grottoes without success before you finally locate a treasure chest. You conclude that the probability you will have to investigate at most x grottoes without success is (x+1) 5 (x+1) and F(5) = 1. (Remember that n) = n(n-1)(n-2)...(n-k+1) is the F(X) = P(X ≤ x) = 1 - number of permutations (ordered lists without replacement) of k items from n possibilities.) a) What is the probability you will have to investigate exactly 3 grottoes without success? b) What is the expected number E(X) of grottoes you will investigate without success? c) What is the variance Var(X) of the number of grottoes you will investigate without success?
6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5 grottoes without success before you finally locate a treasure chest. You conclude that the probability you will have to investigate at most x grottoes without success is (x+1) 5 (x+1) and F(5) = 1. (Remember that n) = n(n-1)(n-2)...(n-k+1) is the F(X) = P(X ≤ x) = 1 - number of permutations (ordered lists without replacement) of k items from n possibilities.) a) What is the probability you will have to investigate exactly 3 grottoes without success? b) What is the expected number E(X) of grottoes you will investigate without success? c) What is the variance Var(X) of the number of grottoes you will investigate without success?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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Transcribed Image Text:6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5
grottoes without success before you finally locate a treasure chest. You conclude that the
probability you will have to investigate at most x grottoes without success is
(x+1)
5
(x+1)
and F(5) = 1. (Remember that n) = n(n-1)(n-2)...(n-k+1) is the
F(X) = P(X ≤ x) = 1 -
number of permutations (ordered lists without replacement) of k items from n possibilities.)
a) What is the probability you will have to investigate exactly 3 grottoes without success?
b) What is the expected number E(X) of grottoes you will investigate without success?
c) What is the variance Var(X) of the number of grottoes you will investigate without
success?
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