Physics 129C, Spring 2010
Problem Set 1 Solution
Chan Y. Park
April 17, 2010
Problem 1
Prove:
n
P (n Ei ) =
i=1
n
P (Ei )
i=1
n
P (Ei Ej )
j>i
P (Ei Ej Ek ) +
+
k>j>i
n1
+ (1)
P (E1 E2 En )
Solution:
Lets prove the given relation by mathematical inducti
Physics 129c
Problem Set Number 5
Due Wednesday, May 5, 2010
Reading: Finish reading the note (posted on the course web page) on Point
Estimation.
20. Suppose we wish to measure the area of a rectangle using measurements
of its length and width. Let the j
Physics 129C, Spring 2010
Problem Set 4 Solution
H.-J. Chung
May 9, 2010
Problem 16
Use acceptance-rejection to generate random numbers for a PDF constructed as follows: Draw a
circle of radius ve centered at (x, y) = (5, 1). The PDF is given by that part
Physics 129C, Spring 2010
Problem Set 5 Solution
Chan Y. Park, Frank Porter
May 18, 2010
Problem 20
Suppose we wish to measure the area of a rectangle using measurements of its length and width.
Let the joint PDF for the length and width measurements be:
Physics 129C, Spring 2010
Problem Set 8 Solution
H.-J. Chung, Frank Porter
June 7, 2010
Problem 32
It is often dicult to evaluate coverage of a method for interval estimation. In such cases, we often
resort to simulations. Well do an example where you act
Employer Statement E01
2. Claimants Name
1. Return to:
Division of Temporary Disability Insurance
PO Box 387
Trenton, NJ 08625-0387
5. Employer Name :
Singh, Manvir
3. Date Disability Began
4. Soc Sec No
826-70-4124
2/6/2016
6. Form Identification Number
Singh 1
Manvir Singh
Professor Romila Vaswani
English- 122-77
10/17/2015
Motives Behind Wildlife Hunting:
Hunting is the method of killing or trapping any animal, or coming after with the
intent of doing so. Hunting is widely famous as our ancestors used
Singh 1
Manvir Singh
Professor Romila Vaswani
English- 122-77
10/17/2015
Motives Behind Wildlife Hunting:
Hunting is the method of killing or trapping any animal, or coming after with the
intent of doing so. Hunting is widely famous as our ancestors used
Abdurahman Sherif
Homework 2: Coupon Collector
Instructions
Think of an urn with n balls numbered from 1 to n. Sampling with replacement: A ball is drawn,
its number is recorded, then the ball is returned.
1. How many draws does it take on averag
Singh 1
Manvir Singh
Professor Romila Vaswani
English- 122-77
10/17/2015
Motives Behind Wildlife Hunting:
Hunting is the method of killing or trapping any animal, or coming after with the
intent of doing so. Hunting is widely famous as our ancestors used
Physics 129C, Spring 2010
Problem Set 9 Solution
H.-J. Chung, Chan Y. Park, Frank Porter
June 8, 2010
Problem 36
Problem 33 illustrated a situation in which a particular statistic sometimes carries no information
on the hypothesis to be tested. This examp
Physics 129c
Problem Set Number 9
Due Wednesday, June 2, 2010
Reading: Read the note (posted on the course web page) on Density Estimation.
This is the last problem set for Ph 129c, due to the shortened quarter.
36. Problem 33 illustrated a situation in w
Physics 129c
Problem Set Number 2
Due Wednesday, April 14, 2010
Reading: Read the note (posted on the course web page) on Simulation.
6. Exercise 7 in the Probability course note.
7. Exercise 8 in the Probability course note. You are not required to get
a
Physics 129c
Problem Set Number 3
Due Wednesday, April 21, 2010
Reading: Read the note (posted on the course web page) on Bayes and
Neyman. This note discusses philosophical issues underlying what we do
when we quote results of our measurements. This is a
Physics 129C, Spring 2010
Problem Set 3 Solution
Chan Y. Park
April 27, 2010
Problem 11
The random walkshows up in various forms in physical situations. Consider a simple onedimensional random walk with xed step size a. That is, each step in our random wa
Physics 129C, Spring 2010
Problem Set 2 Solution
H.-J. Chung, F. Porter
April 26, 2010
Problem 6
Prove the Chebyshev inequality for a discrete distribution.
Solution:
We want to show that P (|X | > n)
1
n2
holds for a discrete distribution.
P (|X | > n)
Physics 129c
Problem Set Number 4
Due Wednesday, April 28, 2010
Reading: Start to read the note (posted on the course web page) on Point
Estimation.
16. Use acceptance-rejection to generate random numbers for a PDF constructed as follows: Draw a circle of
Physics 129c
Problem Set Number 6
Due Wednesday, May 12, 2010
Reading: Start reading the note (posted on the course web page) on Interval
Estimation. You may nd this note somewhat rough going, as the details
may come across as convoluted. Try to read up t
Physics 129c
Problem Set Number 7
Due Wednesday, May 19, 2010
Reading: Finish reading the note (posted on the course web page) on Interval Estimation.
28. Lets nish our kaon eciency calculation. You have code that generates the entire event, including det
Physics 129C, Spring 2010
Problem Set 6 Solution
H.-J. Chung, Frank Porter
May 22, 2010
Problem 24
We described the case study of measuring an asymmetry parameter (section 4.4 of the note on
Point ) on CP violation via mixing. The substitution method esti
Physics 129c
Problem Set Number 8
Due Wednesday, May 26, 2010
Reading: Read the note (posted on the course web page) on Hypothesis
Testing. Try to read the rather long section 6.7 to get the general ideas,
without getting bogged down in the details.
32. I
Physics 129C, Spring 2010
Problem Set 7 Solution
Chan Y. Park, Frank Porter
May 26, 2010
Problem 28
Lets nish our kaon eciency calculation. You have code that generatesthe entire event, including
detector resolution. All that remains is to apply the event
Physics 129c
Problem Set Number 1
Due Wednesday, April 7, 2010
Reading: Read the note (posted on the course web page) on Probability.
1. Exercise 3 in the Probability course note.
2. Exercise 4 in the Probability course note.
3. Exercise 5 in the Probabil