Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
Probability
Stat 131A
Hank Ibser
Notation and Denitions
A = an event which may or may not occur (A)
Ac = the complement, or opposite, of event A (A complement)
P (A) = the probability that event A occurs (probability of A)
P (BA) = the conditional probab
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Solution of Assignment 1
I The practical problem
400
300
100
200
passengers (in thousands)
500
600
1.
Jan 50
Jan 52
Jan 54
Jan 56
Jan 58
Jan 60
time
Figure 1: Monthly totals (in thousands) of international airline passengers from January
1949 to December
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Midterm One
Statistics 153, Spring 2014
06 March, 2014
1. Two quarterly time series data sets are plotted below. There are 36 observations (quarterly data for 9
years) in each data set. It is believed that for one of the two data sets, the model:
Xt = (a
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
Hank Ibser Statistics 131 Spring 2015
Study Guide for the Midterm
The midterm (Wednesday March 11 in lecture) will cover the following
chapters with certain parts omitted:
Ch12: Concepts and terminology in these chapters will be included as
relevant to C
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
Statistics 131A, Summation and Correlation
The correlation coecient r can be written either
1 n (xi x) (yi y )
n i=1
SDx
SDy
n
i=1
1
n
or
xi y i xy
SDx SDy
The proof is as follows:
1 n (xi x) (yi y )
n i=1
SDx
SDy
=
=
=
=
=
n
1
n SDx SDy
1
SDx SDy
1
n
n
i
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Homework One
Statistics 131a
1. Consider simple linear regression where there is one response variable y and an
explanatory variable x and there are n subjects with values y1 , . . . , yn and x1 , . . . , xn .
a) Write down (no need to calculate) the leas
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
STUDENTS NAME (please print) :
Takehome MATH 282A Fall 2014
Takehome examopen book but please work alone. Prove all your statements; all subproblems have equal weight.
Part I amounts to 70%. It is due Friday Dec 12 in class!
Part II amounts to 30%.
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Homework 3
Due date: 9/18
Problem 1
Refer to Problem 6 in HW2. (This is the second part of this problem.)
We now turn to simulation work. Use the data (or a subpart of it) to compute a covariance matrix
(say 0 ) for your assets and a vector of mean return
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
1. Consider the time series Xt = 1 + 0.5t + Wt where Wt W N (0, 2 ) and let Yt be the
5point moving average dened by Yt = 1 2
j=2 Xt+j .
5
(a) (2 points) Give the mean function of Xt (i.e. X (t) = E(Xt ).
Solution: X (t) = E(Xt ) = 1 + 0.5t + EWt = 1 + 0
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Midterm One
Statistics 153, Spring 2014
15 May, 2014
1. Two quarterly time series data sets are plotted below. There are 36 observations (quarterly data for 9
years) in each data set. It is believed that for one of the two data sets, the model:
Xt = (a +
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Elements of Forecasting
in Business, Finance, Economics and Government
Francis X. Diebold
Department of Economics
University of Pennsylvania
Solutions Manual
Copyright F.X. Diebold. All rights reserved.
2
Preface
This is quite a nonstandard Solutions Ma
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Homework 2
Due date: 9/11
Problem 1 Do Problem 4 on p.490 in Ruppert
Problem 25 Do Problems 1,2,3,5 in Section 16.11 in Ruppert
Problem 6 This problem is designed to make you investigate the behavior of naive Markowitz portfolios in practice. Consider th
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Time Series
H ILARY T ERM 2010
P ROF. G ESINE R EINERT
http:/www.stats.ox.ac.uk/~reinert
Overview
Chapter 1: What are time series? Types of data, examples, objectives. Definitions, stationarity and autocovariances.
Chapter 2: Models of stationary proces
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
6
Stationary Models
6.1 Purpose
As seen in the previous chapters, a time series will often have welldened
components, such as a trend and a seasonal pattern. A wellchosen linear regression may account for these nonstationary components, in which case t
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Homework 1
Due date: 9/3
Note: reading chapters 4 and 5 of the book will help refresh your memory concerning some of the
methods needed in this homework.
Problem 1 Download 5 years of daily data for two stocks of your choice. Create a dataset of daily
ret
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Estimation of ARMA Models
Eric Zivot
April 6, 2005
1
Maximum Likelihood Estimation of ARMA Models
For iid data with marginal pdf f (yt ; ), the joint density function for a sample y =
(y1 , . . . , yT ) is simply the product of the marginal densities for
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Handout 1
Stat 131 Linear
Models
Sep 2, 2015
Facts about Matrices
We shall write A to mean the determinant of a square matrix A. We shall also introduce a new function
n
of a matrix called trace, written as Tr(A), dened as the sum of the diagonal entrie
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
Psychology 8815
Prof. Federico
The Mathematical Derivation of Least Squares
Back when the powers that be forced you to learn matrix algebra and calculus, I
bet you all asked yourself the ageold question: When the hell will I use this
stuff? Well, at long
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Fall 2014
OLS in Matrix Form
1
The True Model
Let X be an n k matrix where we have observations on k independent variables for n
observations. Since our model will usually contain a constant term, one of the columns in
the X matrix will contain only ones. This col
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Expected Values, Standard
Errors, Central Limit Theorem
FPP 1618
Statistical inference
Up to this point we have focused primarily on
exploratory type statistical analyses (with a little
probability thrown in).
We will now dive into the realm of statist
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Econ 522 Lecture 10 (Oct 7 2008)
Before we start, a quick example, not directly related to the course, on how economists
look at the world differently than everyone else.
Theres a wellpublicized story recently of a 90yearold woman in Akron, Ohio, Addie
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
WEB NOTES
Sixth Edition
The following are the web notes for the sixth edition of Law and Economics by Robert D.
Cooter and Thomas S. Ulen. Our intent in these notes is to extend the material in the text by
describing some additional issues, articles, case
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Overview: The Process That Feeds Biosphere
Autotrophs sustain themselves w/o eating
anything derived from other organisms
produce organic mol from inorganic mol (i.e. CO 2)
Photoautotrophs use energy of sunlight to make
organic mols (photosyn.)
plants
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Expectation Damages
Contracts Prof. Merges
April 5, 2011
Expectation in depth
Loss in value plus other loss
Rest. 2d formula
Concepts:
Loss in value
Other loss,
Minus cost avoided (i.e., saved by breach)
What do these terms mean?
Loss in value = di
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Econ 522
Economics of Law
Dan Quint
Fall 2015
Lecture 15
Reminders
HW3 due next Thursday (November 12) at midnight
Second midterm Wednesday November 18 in class
2
Lets recap our
story so far
3
Our story so far
Efficiency
Maximizing total surplus realiz
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Problem Set 2
Aniket Kesari & Kyle
DeLand Due Oct. 12
Problem 1: Ecient Breach
Sal (S) promises to provide a unique widget to Beauregard (B1),
and B1 promises to pay $200 to S upon delivery of the widget.
Then, another potential buyer (B2) appears. B2 may
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
CONTRACTS
I. Remedies
A. Expectation damages are the standard measure of damages of promissory
liability both for actions based on the bargain theory and those based on
promissory estoppel. They put the promisee in as good a position as he
would have been
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Overview: Life at the Edge
Plasma Membrane
8nm thick boundary that separates the
living cell from its surroundings
exhibits selective permeability, allowing
some substances to cross it more easily
than others
general principles of membrane traffic
appl
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
UCSC AMS 5
Quiz 3 Solutions
Summer Session I, 2015
1. A large (hypothetical) study of the relationship between parental income and IQs of their children
yielded the following statistics.
average income $90, 000,
average IQ 100,
SD $45, 000
SD 15,
r 0.5
(a