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 increasing steadily faster than the rate of population
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 outcome of an experiment, but instead
with some function
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.
7.1.1
Uniform discrete random variable
This is a random
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 of the same cereal from California weighed 11.59 ounce
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 these 6 questions are worth 130 points in all. And you tot
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 questions are worth 130 points in all. And you total score
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 repair Ralphs vacuum cleaner. Motor #1 has a 65% chance
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
otherwise.
(a) Find the marginal densities of X and Y .
(b)
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 or 1, the second was 0 or 1, and the third was anythin
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 by 11 paper).
Calculator, and
Blue book for writing all
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 is easiest if we sort the data into a table in order to
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 that an insect has only
this genotype, and no others. For
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
43
71
38
9
65
86
35
26
15
45
44
0
44
38
18
5
27
53
0
29
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:
a. Percent of premium expenses are 10% per year.
b. Pe
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 = 0.02
100 x t
Find 10 p 50()
SOLUTION
10 p
()
50
= exp
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 endowment insurance policy of 1000 is issued to (x)
and has
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 weighed 11.59 ounces on average. Ralph Nader
wants us to dete
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 random variable indicates its weighted average.
Ex. How
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 and Alternative Hypotheses . . . . . . . . . . . . . .
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 mechanical system contains 8 components. If there is a 18% ch
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 ) = T (T (v ) = V
0
det (A1) = 1/det (A)
A
1 = det (I)
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 asked them whether they liked apple pie. Suppose that
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 pair of random variables X and Y with joint distributi
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 a measurement X with probability density function
x
P
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 random variable with density
fX (x) = 12x3 (1 x2 )
whe
PSTAT W 120A:
Assignment 4B
Due Monday, August 31, 2015
Please write up your solutions and submit them online by the end of the day on Monday.
Lesson 15 Cumulative Distribution Function
1. The CDF of our random variable X is
F (t) =
t2
15 25t + 15t2 3t3
4
PSTAT 172 B
Revision Problems with Solutions
Ian Duncan, FSA FIA FCIA MAAA
[email protected][email protected]
University of California, Santa Barbara
1
1.
SOLUTION
Note; recall that t q 40.5 = t. q 40.5 and
t q x+s
x+s+t = t q x+s and t q x+s
PSTAT W 120A:
Assignment 5.a
Due Wednesday September 2, 2015
Please write up your solutions and submit them online by the end of the day on Wednesday.
Lesson 17 Geometric Uniform Random Variables
1. A house sits in the center of a 300 m by 300 m square lo
PSTAT W 120A:
Assignment 6
Due Wednesday September 9, 2015
Please write up your solutions and submit them online by the end of the day on Wednesday.
Lesson 21 Conditional Expectations
1. Suppose that R and S have a joint probability mass function
S
-1
R
0
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
T2x, y = y, 5x, y
T1x, y, z = 3x, y + 2z
T = T1 T2
S
PROBABILITY AXIOMS AND PROPERTIES
LECTURE NOTES
BY MARYANN HOHN
Contents
1.
Definition and Properties
1
2.
Probabilities
3
1. Definition and Properties
Definition 1.1. A sample space, , is a set which represents the collection of all outcomes of
some expe
GER 101C
24./25. April
Tagesprogramm
1. Film: Friendship
2. Midterm: Was die Deutschen ber
Kalifornien denken
3. Artikel diskutieren
4. Quiz
Film - Freundschaft
A) Was haben wir schon gesehen?
Wortschatz
Quiz nchste Woche Montag/Dienstag!
Szene 14:00-
GER 101C
19./20. April
Tagesprogramm
1. Easy German: Amerikas Einfluss
2. Die USA in den Nachrichten
3. Film Freundschaft
4. Midtermprojekte
Welchen Einfluss hat Amerika auf
https:/www.youtube.com/watch?v=hMavMafzSls&spfreload=10
andere Lnder?
Vor dem Se
GER 101C
Tagesprogramm
1. r-Laute
2. Typisch amerikanisch / Redemittel
3. Wortschatz
4. Konjuktionen
5. Rammstein Amerika
6. Vorurteile & Stereotypen
10./11. April
Kinderreime
Konsonante [] oder Vokale []?
Eins, zwei, drei, auf der Strae liegt ein Ei.
Wer