PSTAT 160B Winter 2016
Homework 2
Solve the exercises (1)-(8) below, and submit only the Python exercise (8) on Wednesday January
20. The solution to (1)-(7) will be posted on Gauchospace.
(1) The lifetime of A s dog and cat are independent exponential ra
announcements
Office Hour (change)
M 11:00-12:00 and W 10:30-11:30
Homework 1 is due on Wednesday night.
Homework theoretical exercises will be posted on Tuesday.
Read Chapter 5.
The least quiz score will be dropped in the final grade
consideration.
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Announcement
Please go to Discussion section: Tuesday and
Wednesday
Office Hours:
MW 11:00-12:00 South Hall 5508
Homework: posted on gauchospace
TA:
Javier Zapata : zapata@pstat.ucsb.edu
Seyyed Mousavi : mousavi@pstat.ucsb.edu
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Exponentials
2 / 23
E
Announcement
Overview: PSTAT 160B
This is a continuation from 160A. The topics covered in the
course are Continuous models; Continuous time stochastic
processes: Poisson process, Markov chains, Brownian motion,
simulation of these processes and their appl
PSTAT 160B, Winter 2015. Homework 1
(1). We want to compute the expectation of T =
6
X
Xi , where Xi Exp() is the service
i=1
time of the i -th customer, i = 1, 2, 3, 4, 6 . Note that you are the sixth customer. Although the
first customer is already serv
PSTAT 160B Winter 2016
Homework 7
Solve the exercises (1)-(6) below, and submit only the Python exercise (7) on Wednesday March 9th.
The solution to (1)-(6) will be posted on Gauchospace.
(1) Suppose that the interarrival distribution for a renewal proces
PSTAT 160B, Winter 2015. Homework 6
(1). A job shop consists of three machines and two repairmen. The amount of time a machine
works before breaking down is exponentially distributed with mean 10. If the amount of time it
takes a single repairman to fix a
PSTAT 160B Winter 2016
Homework 2
Solve the exercises (1)-(8) below, and submit only the Python exercise (8) on Wednesday January
20. The solution to (1)-(7) will be posted on Gauchospace.
(1) The lifetime of A s dog and cat are independent exponential ra
PSTAT 160B Winter 2016
Homework 5
Solve the exercises (1)-(9) below, and submit only the Python exercise (10) on Wednesday February
17th. The solution to (1)-(9) will be posted on Gauchospace.
(1) What is the distribution of B(s) + B(t) for s t ?
Solution
PSTAT 160B Winter 2016
Homework 4
Solve the exercises (1)-(10) below, and submit only the Python exercise (10) on Wednesday February
10th. The solution to (1)-(9) will be posted on Gauchospace.
(1) A two dimensional Poisson process is a process of randoml
Announcements
Homework 2 (due tonight).
Solution to Theoretical Parts is posted.
Homework 3 (due next Wed. night)
Please go to Discussion Sections.
Quizzes,
Read Chapter 5 of the textbook.
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Review
2 / 18
Poisson Process
()
A counting process X is ca
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Poisson Process
A counting process X () is called a Poisson process with rate
(intensity) , if
(1) X (t ) X (s ) is independent of F (s ) ;
(2) X (t ) X (s ) has the same probability distribution as
X (t s ) for 0 s t < 1 ; and
(3) X (t ) is distri
PSTAT 160B Winter 2016
Homework 4
Solve the exercises (1)-(10) below, and submit only the Python exercise (10) on Wednesday February
10th. The solution to (1)-(9) will be posted on Gauchospace.
(1) A two dimensional Poisson process is a process of randoml
PSTAT 160B Winter 2016
Homework 3
Solve the exercises (1)-(8) below, and submit only the Python exercise (8) on Wednesday January
27. The solution to (1)-(7) will be posted on Gauchospace.
(1) Customers arrive at a bank at a Poisson rate . Suppose two cus
PSTAT 160B Winter 2016
Homework 5
Solve the exercises (1)-(9) below, and submit only the Python exercise (10) on Wednesday February
17th. The solution to (1)-(9) will be posted on Gauchospace.
(1) What is the distribution of B(s) + B(t) for s t ?
Solution
PSTAT 160B, Winter 2015. Homework 6
(1). A job shop consists of three machines and two repairmen. The amount of time a machine
works before breaking down is exponentially distributed with mean 10. If the amount of time it
takes a single repairman to fix a
Yunpeng Huang
Pstat 160B
HW 7
import matplotlib.pyplot as plt
import numpy as np
import random
t1 = 0
for i in range(1000):
c1 = []
while (len(c1) < 10):
t1 += 1
a = np.random.randint(0,10)
if (1 - c1.count(a):
c1.append(a)
else:
c1 = [a]
t1 = t1/1000.0
p
PSTAT 160 B Practice Final Winter 2016
180 minutes. Instructor: Tomoyuki Ichiba.
Write your name and all your answers clearly in the answer sheet.
1. Cars arrive to a single pump gas station according to a Poisson process with rate 3 cars per
hours. If a
PSTAT 160B Winter 2016
Homework 5
Solve the exercises (1)-(9) below, and submit only the Python exercise (10) on Wednesday February
17th. The solution to (1)-(9) will be posted on Gauchospace.
(1) What is the distribution of 3(5) + 3(t) for s S t ?
Soluti
PSTAT 160B Winter 2016
Homework 3
Solve the exercises (1)-(8) below, and submit only the Python exercise (8) on Wednesday January
27. The solution to (1)-(7) will be posted on Gauchospace.
(1) Customers arrive at a bank at a Poisson rate . Suppose two cus