a) Suppose that people arrive at a bus stop in accordance with a Poisson process with rate 2. The bus departs at time 1. Let x denote the total amount of waiting time of all those that get on the bust at time 1. We want to determine Var (X ). Let N (1) denote the number of arrivals by time 1. i) What is E[X | N (1)] ? ii) Argue that Var [X | N (1)] = N (t)t² /12 . iii) What is Var (X ) ?
a) Suppose that people arrive at a bus stop in accordance with a Poisson process with rate 2. The bus departs at time 1. Let x denote the total amount of waiting time of all those that get on the bust at time 1. We want to determine Var (X ). Let N (1) denote the number of arrivals by time 1. i) What is E[X | N (1)] ? ii) Argue that Var [X | N (1)] = N (t)t² /12 . iii) What is Var (X ) ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose that people arrive at a bus stop in accordance with a Poisson process with rate
2. The bus departs at time t. Let x denote the total amount of waiting time of all
those that get on the bust at time t. We want to determine Var (X ). Let N (t) denote
the number of arrivals by time 1.
5. а)
i)
What is E[X | N (t)] ?
Argue that Var [X | N (t)] = N (t)t² / 12 .
What is Var (X ) ?
ii)
iii)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb1f115b-cbb4-4f96-a28c-b814570ea454%2F89c616c0-e468-4b44-9059-318038a2f966%2Fkeymm2s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that people arrive at a bus stop in accordance with a Poisson process with rate
2. The bus departs at time t. Let x denote the total amount of waiting time of all
those that get on the bust at time t. We want to determine Var (X ). Let N (t) denote
the number of arrivals by time 1.
5. а)
i)
What is E[X | N (t)] ?
Argue that Var [X | N (t)] = N (t)t² / 12 .
What is Var (X ) ?
ii)
iii)
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