Neel Sabnis
Honors Seminar INT84ZA
Jordan Clark, Bob Wilkinson
June 7, 2014
Desalination and the Water Supply
Fresh water makes up approximately 2.5% of the worlds water supply and the demand
for this
PSTAT 120A: Probability and Statistics
Fall 2014
Lecture 7: Week 7
Lecturer: Wenjian Liu
7.1
Scribes: WL
Special discrete random variables
We will now look at some famous probability mass functions.
7
PSTAT 120A: Probability and Statistics
Fall 2014
Lecture 4: Week 4
Lecturer: Wenjian Liu
4.1
4.1.1
Scribes: WL
Random Variables
Introduction
In many situations we are not concerned directly with the o
Wenjian Liu (Instructor)
PSTAT 120A Fall 2014
Homework 5
Due Monday, Nov 24, 2014
Problem 5.1
Let X and Y be continuous random variables with joint density function
2 y
if 0 x y,
e
f (x, y) =
0
othe
PSTAT 120C:
Assignment 3
Due January 29, 2015
These problems will be due in lecture next Thursday.
1. A sample of 453 boxes of cereal from New York weighed 12.03 ounces on average. A sample
of 5 boxes
PSTAT 120A
Probability and Statistics
Fall 2014
Midterm Examination Practice 2
P#1
20
P#2
20
P#3
20
P#4
20
P#5
20
P#6
30
Total 100
Please note that the full credit of this midterm is 100, although the
PSTAT W 120A:
Assignment 1.b
Due Monday Aug. 10, 2015
Please write up your solutions and submit them online by the end of the day on Monday.
Lesson 3 Bayes Rule
1. There are three motors available to
PSTAT 120A
Probability and Statistics
Spring 2015
Midterm Examination
P#1
20
P#2
20
P#3
20
P#4
20
P#5
20
P#6
30
Total 100
Please note that the full credit of this midterm is 100, although these 6 ques
PSTAT 120C:
Practice Questions
Midterm on February 5, 2015
The midterm exam is next Thursday during lecture.
Please be sure to bring
One formula sheet (you may write on two sides of one piece of 8.5
Wenjian Liu (Instructor)
PSTAT 120A Fall 2014
Homework 2
Due Monday, Oct 20, 2014
Problem 2.1
Before the early 1990s, a telephone area code in the US consisted of three digits, where the rst was
not 0
PSTAT 120C:
Practice Questions
Midterm on February 5, 2015
The midterm exam is next Thursday during lecture.
Here are the solutions to the practice questions.
1. These are two independent samples. It
PSTAT 172 B
HOMEWORK: PREMIUMS
April 4 2014
Ian Duncan, FSA FIA FCIA MAAA
[email protected][email protected]
1
1. For a fully-discrete whole life insurance of 100,000 on (35) you are given:
PSTAT 172 B
Homework April 18
(hand in April 25)
Ian Duncan, FSA FIA FCIA MAAA
[email protected][email protected]
University of California, Santa Barbara
1
1. A fully-discrete, 3-year endow
PSTAT 120A: HW1 - Solutions
Problem 1. A biologist is studying the appearance of three genotypes, denoted by A, B and C,
in certain insects. For each of the three genotypes, the probability is 0.1 tha
PSTAT 172 B
MULTIPLE DECREMENTS
Homework with Solutions
Ian Duncan, FSA FIA FCIA MAAA
[email protected][email protected]
University of California, Santa Barbara
1
1. Given (1)t =
_2_
(2)t
PSTAT 120C:
Solutions for Assignment #5
February 19, 2015
1. The following data on the number of incident reports led at two police stations was collected
over a number of weeks.
Station 1
Station 2
4
PSTAT 120C:
Solutions to Assignment # 3
February 2, 2015
1. A sample of 453 boxes of cereal from New York weighed 12.03 ounces on average. A sample
of 5 boxes of the same cereal from California weighe
PSTAT 120A: Probability and Statistics
Fall 2014
Lecture 6: Week 6
Lecturer: Wenjian Liu
6.1
6.1.1
Scribes: WL
Expectation and Variance
Expectation for a Discrete Distribution
The expected value of a
PSTAT 120C
PROBABILITY AND STATISTICS
Vasudevan Mangalam
Department of Statistics and Applied Probability
University of California, Santa Barbara
Contents
1 Testing Statistical Hypotheses
1.1 The Null
PSTAT 120A
Probability and Statistics
Fall 2014
Final Examination Practice 2
P#1
10
P#2
10
P#3
10
P#4
10
P#5
15
P#6
15
P#7
10
P#8
10
P#9
10
P#10
20
Total
100
Please note that the full credit of this n
PSTAT 120A
Probability and Statistics
Fall 2014
Final Examination Practice 1
P#1
10
P#2
10
P#3
10
P#4
15
P#5
10
P#6
10
P#7
10
P#8
15
P#9
10
P#10
20
Total
100
Please note that the full credit of this n
T1: R3 R2
T2x, y = y, x, 5y
T1x, y, z = 2x, y + 3z
T = T1 T2
S = T2 T1
T x, y = T1y, x, 5y = 2y, x + 15y
S x, y, z = T22x, y + 3z = y + 3z, 2x, 5y + 15z
T = T1 T2: R2 R2
S = T2 T1: R3 R3
T1: R3 R2
44
V
n
R
44
aij = 0
n = 10.
U
T
a
0
0
0
b
e
0
0
c
f
h
0
R10.
w Range(T )
w ker (T ).
i > j.
d
g
= a, b, c, d, e,
i
j
f , g, h, i, j
T2 = 0
T: V V
(T )
T
T (T (v ) = V
0
(T )
V
v
T (v ) = w
T (w
PSTAT W 120A:
Assignment 3A
Due Wednesday Aug. 19, 2015
Please write up your solutions and submit them online by the end of the day on Wednesday.
Lesson 9 Joint Distributions
1. Suppose that we have a
PSTAT W 120A:
Assignment 2.a
Due Wednesday Aug. 12, 2015
Please write up your solutions and submit them online by the end of the day on Wednesday.
Lesson 5 Binomial Experiments
1. A complicated mechan
PSTAT W 120A:
Assignment 2.b
Due Monday August 17, 2015
Please write up your solutions and submit them online by the end of the day on Monday.
Lesson 7 Poisson Approximation
1. A survey of 3300 people
PSTAT W 120A:
Assignment 3.b
Due Monday August 24, 2014
Please write up your solutions and submit them online by the end of the day on Monday.
Lesson 11 Variance
1. We have an experiment that produces
PSTAT W 120A:
Assignment #4.a
Due Wednesday August 26, 2015
Please write up your solutions and submit them online by the end of the day on Wednesday.
Continuous Random Variables
1. Suppose that X is a
MIDTERM EXAM A
PSTAT 120A - Winter 2014
By writing my name and signing below I swear that I have not engaged in any form of
academic dishonesty or cheating.
Name:
Signature:
Section meeting time:
Do
FINAL EXAM A
PSTAT 120A - Winter 2014
By writing my name and signing below I swear that I have not engaged in any form of
academic dishonesty or cheating.
Name:
Signature:
Section meeting time:
Do no
PSTAT 120B, Spring 2017
Homework 7
due on June 15 during Final Exam
1. Let p denote the portion of a students exam with errors. Suppose we test H0 : p = 0.05 and
Ha : p > 0.05 using the following rule
PSTAT 120B, Spring 2017
Homework 6
due on June 5 in class
1. Suppose X1 , X2 , . . . , Xn are i.i.d. random variables such that x [0, 1] and has the following density function:
f (x | ) =
(2)
[x(1 x)]
Midterm Exam
PSTAT 120B, Spring 2017
iid
1. Let X1 , X2 , . . . , Xn N ( x , x2 ): i.e., X1 , X2 , . . . , Xn follow the normal distribution with mean x and
variance x2 . Let X be the sample mean:
1
X
PSTAT 120B, Spring 2017
Homework 5
due on May 24 in class
1. Suppose that independent random samples of n1 = n2 = 30 adults were selected for comparing mineral
intake. Mean and standard deviation inta
PSTAT 120B, Spring 2017
Homework 3
Due in class on May 1, 2017
1. Suppose X Poisson(), Y Poisson(), and that X and Y are independent. Let Z = X + Y . Prove
that Z Poisson( + ) via both of the followin