A poll of frequent travelers asked them what they preferred for in-flight amenity if they could have one of the items on the list for no extra charge. The joint probability distribution describing the poll results is shown in the matrix below.What proportion of respondents were children? Are the two poll variables (Age and Preference) independent? How can you tell? Given a traveler is young, what is the probability that traveler’s preference is wi-fi? Given a traveler is not a child, what is the probability the traveler prefers video or wi-fi (stated differently, the preference isn’t a consumable: a meal or alcohol)? The response matrix indicates there is an easy choice of which item to make available to travelers for free. What is the item and why is the choice of this item an easy one? МealAlcohol VideoWifiType of TravelerChildren.08.04.02.04YoungMiddle aged.12.02.04.12.04.08.04Old.14.02.12.08

Type of traveler Meal Alcohol Video Wifi Total Children 0.08 0 0.04 0.02 0.14 Young 0.12 0.02 0.04 0.04 0.22 Middle aged 0.12 0.04 0.08 0.04 0.28 old 0.14 0.02 0.12 0.08 0.36 Total 0.46 0.08 0.28 0.18 1 1) The proportion of respondents were children: = n(c) = 0.14 2) Are the two poll variables (Age and Preference) independent? How can you tell? : No, the two poll variables are not independent because, P(travel|meal) ≠P(travel) Hence they are dependent. 3) Given a traveler is young, what is the probability that traveler’s preference is wi-fi : = p(W | Y) = P(W ∩ Y)/P(Y) = 0.04/0.22 = 0.1818 4) Given a traveler is not a child, what is the probability the traveler prefers video or wi-fi (stated differently, the preference isn’t a consumable: a meal or alcohol): P1 = P(Prefer wifi given traveler is not child) = (0.04+0.04+0.08) / (0.22+0.28+0.36) = 0.1860 P2 = P(Prefer Video given traveler is not a child) = (0.04+0.08+0.12)/ (0.22+0.28+0.36) = 0.2791 Required probability = P1+P2 = 0.1860+0.2791 = 0.46515) The response matrix indicates there is an easy choice of which item to make available to travelers for free. What is the item and why is the choice of this item an easy one: The item to make available to travelers for free is meal Because it has highest probability among all items

Answered: A poll of frequent travelers asked them…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A poll of frequent travelers asked them what they preferred for in-flight amenity if they could have one of the items on the list for no extra charge. The joint probability distribution describing the poll results is shown in the matrix below.

What proportion of respondents were children?

Are the two poll variables (Age and Preference) independent? How can you tell?

Given a traveler is young, what is the probability that traveler’s preference is wi-fi?

Given a traveler is not a child, what is the probability the traveler prefers video or wi-fi (stated differently, the preference isn’t a consumable: a meal or alcohol)?

The response matrix indicates there is an easy choice of which item to make available to travelers for free. What is the item and why is the choice of this item an easy one?

Мeal
Alcohol Video
Wifi
Type of Traveler
Children
.08
.04
.02
.04
Young
Middle aged
.12
.02
.04
.12
.04
.08
.04
Old
.14
.02
.12
.08

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