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
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

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 2014
Department of Economics
University of California
Berkeley
Spring 2017
Economics 100B
Professor Olney
Memo Regarding the Final
Comprehensive Essay: Due on bCourses, Tuesday, May 2, 8:00 a.m. (No late submissions)
Final Exam: Monday May 8, 3:00  6:00 p.m.,
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Department of Economics
University of California, Berkeley
Economics 100B Problem Set #5 Solutions
Spring 2017
Professor Olney
Page $ of 9
Suggested Solutions for Problem Set #5
1
1. (2 points total)
The Phillips Curve equation can be described by the equ
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Department of Economics
University of California, Berkeley
Economics 100B Problem Set #2 Solutions
Spring 2017
Professor Olney
Page # of 8
Suggested Solutions for Problem Set #2
11. (1 point; point each)
Starting from our usual production function
a.
Y
K
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Department of Economics
University of California
Berkeley
Spring 2017
Economics 100B
Professor Olney
PROBLEM SET #4 (2 % of grade; 10 points possible)
DUE: At Wed or Thurs section, March 15 or 16
Problem sets lose 5 points if they are turned in after the
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Department of Economics
University of California
Berkeley
Spring 2017
Economics 100B
Professor Olney
PROBLEM SET #5 (2 % of grade; 10 points possible)
DUE: At Wed or Thurs section, April 19 or 20
Problem sets lose 5 points if they are turned in after the
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
UGBA 118: International Trade
The Ricardian Model Exercises
Multiple Choice Questions
1.
A country engaging in trade according to the principles of comparative advantage gains from trade because it:
a.
b.
c.
d.
e.
2.
Is producing exports using fewer labor
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Catherine Wu
The Fed implemented a federal funds rate roughly 12 percentage points lower than the
policy rule recommended during the mid2000s. Therefore, the Fed didnt follow the Taylor Rule
prior to the crisis. During the financial crisis, the Federal
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Measures of Center
Gaston Sanchez
Creative Commons Attribution ShareAlike 4.0 International CC BYSA
Descriptive Statistics
Gaston Sanchez
2
1 Frequency Tables
2 Charts & Graphics
3 Numeric Summaries
Gaston Sanchez
3
measures
of center
looking for a
midd
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
UGBA 118: International Trade
Imperfect Competition and Economies of Scale Model Exercises
Detailed Solutions for Analytical Problems 1, 2 and 3
P
Domestic Market
A monopoly firm operating in its domestic
market is a price setter and will face a
downward
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
MONDAYS
8:00 AM
9:30 AM
10:00 AM
WEDNESDAYS
Philip Brown Stat
20 89 AM
8:30 AM
9:00 AM
TUESDAYS
Josh
Ceribelli
STAT 20
911
Demetra
Tzamaras
Stat 20
9:0011:00AM
THURSDAYS
Rohit Bahirwani
Stats 20 810 AM
Josh
Ceribelli
STAT 20
911
Shruti Jain
STAT 20
1
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
Summary Statistics, Ch 45
average (or mean) = sum of entries / number of entries
SD = rms of deviations from average
SU = (value  average)/SD
Correlation and Regression, Ch 812
r = average of (x in SU)(y in SU)
prediction error = actual value predicted
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
Solutions for my Sample Final
1. a) 17/25
b) 4/5 * 3/4 * 1/3 = 1/5
c) 4/5 * 4/5 * 1/5 = 0.128
d) (8 choose 6) (17/25)^6 (8/25)^2 = .283
2. a) Weight is at 90th percentile, which is about 23.5 pounds.
Height is predicted to be 1.3 * 0.64 = 0.83 SDs above a
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
Summary Statistics, Ch 45
average (or mean) = sum of entries / number of entries
SD = rms of deviations from average
SU = (value  average)/SD
Correlation and Regression, Ch 812
r = average of (x in SU)(y in SU)
prediction error = actual value predicted
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2015
Summation, Average, and Standard Deviation
Statistics 131, Hank Ibser
Denitions and Formulas
Lists of numbers are often written as xi . Each number on the list is one of
these xi values. Thus the list 1, 4, 6 would have x1 = 1, x2 = 4, and x3 = 6.
Here ar
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
# 7. Imperfect Competition and Economies of Scale Model
a. Incorrect. Internal economies of scale give large firms a cost
advantage over small firms, and lead to an imperfectly competitive
market structure. External economies of scale typically leads to m
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
More about
Correlation
Gaston Sanchez
Creative Commons Attribution ShareAlike 4.0 International CC BYSA
Study the relationship
between X and Y
Gaston Sanchez
Correlation
Coefficient
Correlation Coefficient
Summary statistic that measures
the strength of
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Data and Variables
Gaston Sanchez
Creative Commons Attribution ShareAlike 4.0 International CC BYSA
Statistics is.
gastonsanchez.com
2
Ordinary use
In ordinary conversations, the
word statistics is used as a term
to indicate a set or collection of
numer
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Sample Surveys
Gaston Sanchez
Creative Commons Attribution ShareAlike 4.0 International CC BYSA
Sampling
Chapter 19
Often we want to know
something about the population
But we dont have access to all
of its individuals
Gaston Sanchez
Population
Gender o
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Introduction to R
and RStudio
Gaston Sanchez
Creative Commons Attribution ShareAlike 4.0 International CC BYSA
Statistical Software
2
3
Creators of R
Ross Ihaka
PhD at Berkeley
Gaston Sanchez
Robert Gentleman
PhD at UW
4
Auckland University, New Zealand
Introduction to Probability and Statistics for Life Scientists
STAT 131A

Spring 2014
Regression Errors
Gaston Sanchez
Creative Commons Attribution ShareAlike 4.0 International CC BYSA
How accurate is
regression?
2
The regression method
can be used to predict y
from x
r
e
f
if
d
l
il
w
s
n
io
t
dic
but pre
s
e
lu
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