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...

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