The number of cars that pass through a toll booth on a given highway between 7 and 8 am is distributed Poisson with parameter 15. Each car that passes through the toll booth may or may not be registered and this record is independent of previous records. The probability of being registered is 1/4. Find the joint moment-generating function of the number of registered cars and the number of cars that are not registered.

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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The number of cars that pass through a toll booth on a given highway
between 7 and 8 am is distributed Poisson with parameter 15. Each car
that passes through the toll booth may or may not be registered and this
record is independent of previous records. The probability of being
registered is 1/4. Find the joint moment-generating function of the
number of registered cars and the number of cars that are not registered.
Transcribed Image Text:The number of cars that pass through a toll booth on a given highway between 7 and 8 am is distributed Poisson with parameter 15. Each car that passes through the toll booth may or may not be registered and this record is independent of previous records. The probability of being registered is 1/4. Find the joint moment-generating function of the number of registered cars and the number of cars that are not registered.
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