Each day, two children leave their home at 9am to play along the bank of a stream that runs past their home. Their distance (in metres) upstream from home after t hours is denoted by X(t), and may be reasonably modelled as ordinary Brownian motion {X(t); t>0} with diffusion coefficient o² = 450 m² per hour. (a) Calculate the probability that two hours after leaving home, the children will be within 50 metres of their home. (b) One day, the children are observed 30 metres upstream from their home at 11 am. Calculate the probability that at midday the children will be upstream from their home. (c) On another day, the children are observed to return home at midday. Calculate the probability that at 11 am the children were within 20 metres of their home.
Each day, two children leave their home at 9am to play along the bank of a stream that runs past their home. Their distance (in metres) upstream from home after t hours is denoted by X(t), and may be reasonably modelled as ordinary Brownian motion {X(t); t>0} with diffusion coefficient o² = 450 m² per hour. (a) Calculate the probability that two hours after leaving home, the children will be within 50 metres of their home. (b) One day, the children are observed 30 metres upstream from their home at 11 am. Calculate the probability that at midday the children will be upstream from their home. (c) On another day, the children are observed to return home at midday. Calculate the probability that at 11 am the children were within 20 metres of their home.
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...
Related questions
Question
q7
Transcribed Image Text:Each day, two children leave their home at 9am to play along the bank of a
stream that runs past their home. Their distance (in metres) upstream from
home after t hours is denoted by X(t), and may be reasonably modelled as
ordinary Brownian motion {X(t); t≥ 0} with diffusion coefficient
o² = 450 m² per hour.
(a) Calculate the probability that two hours after leaving home, the
children will be within 50 metres of their home.
(b) One day, the children are observed 30 metres upstream from their home
at 11 am. Calculate the probability that at midday the children will be
upstream from their home.
(c) On another day, the children are observed to return home at midday.
Calculate the probability that at 11 am the children were within
20 metres of their home.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON