1
2/23/15
To understand Gods thoughts we must study statistics, for these are the measure of His
purpose. Florence Nightingale
Normal distribution
Empirical rule N( M: (TL)
0.4
34.1% 34. %
0.0 0.1 0.2 0.3
Measure of relative standing: standard score, al
1
2/20/15
"Youve never heard of the Millennium Falcon? It's the ship that made the Kessel run in less
than 12 parsecs. - Han Solo
Contingency analysis: association between categorical variables
Example 1: The death of adult men and women passengers follow
1/16/15
The man who does not read has no advantage over the man who cannot read.
Mark Twain
Sampling distribution
Example: Let the population be the 20,290 known and predicted genes of the published
genome sequence. We are interested in their lengths.
Hi
1
1/21/15
Never put off till tomorrow what may be done day after tomorrow just as well. - Mark
Twain
Probabiliy
EventA is said to be a subset of event B if a, gawk wet/115 cfw_A A are M50 FA 3-
?enoll b)! A C B
a Asuzs, E=1253 AQLE
, M
E uall likel sim le
1
2/04/15
"Well, that's the news from Lake Wobegon, where all the women are strong, all the men are
good looking, and all the children are above average." Garrison Keillor
Confidence intervals for proportions (the Agresti-Coull method)
.l Xl-Z
l7:-
n+4
l
1/23/15
"Nobody goes there anymore; it's too crowded." - Yogi Berra
Ex2: Jewel wasp
Nasonia vitripennis females can manipulate the sex of the eggs that they lay.
95% female
5% male
Host not Host
parasitized (80% parasitized (20%)
10%
female
Host already S
2/25/15
Procrastination is the art of keeping up with yesterday. Don Marquis
One-sample t-test
Normal human body temperature is 98.6 F. Researchers obtained body temperature
measurements on 25 randomly selected healthy people:
98.4, 98.6, 97.8, 98.8, 97.9
1
1/30/15
What the world needs is more geniuses with humility, there are so few of us left.
-Oscar Levant
Binomial distribution
Let X be the number of succesggm n trials, where the outcome of any single trial is either
success or failure. The trials are i
1
Wart ll '-
2/02/15
"Whats amazing is, if young people understood how doing well in school makes the rest of
their life so much interesting, they would be more motivated. It's so far away in time that they
cant appreciate what it means for their whole li
Problems
373
PROBLEMS
7.1. A player throws a fair die and simultaneously
flips a fair coin. If the coin lands heads, then she
wins twice, and if tails, then one-half of the value
that appears on the die. Determine her expected
winnings.
7.2. The game of C
102
Chapter 3
Conditional Probability and Independence
PROBLEMS
3.1. Two fair dice are rolled. What is the conditional
probability that at least one lands on 6 given that
the dice land on different numbers?
3.2. If two fair dice are rolled, what is the co
50
Chapter 2
Axioms of Probability
which can be generalized to give
n
n
#
&
&
&
P(Ai )
P(Ai Aj ) +
P(Ai Aj Ak )
P Ai =
i=1
i<j
i=1
+ + (1)
n+1
i<j<k
P(A1 An )
If S is finite and each one point set is assumed to have equal probability, then
P(A) =
|A|
|S|
Problems
287
PROBLEMS
6.1. Two fair dice are rolled. Find the joint probability
mass function of X and Y when
(a) X is the largest value obtained on any die and
Y is the sum of the values;
(b) X is the value on the first die and Y is the
larger of the two
224
Chapter 5
Continuous Random Variables
A random variable is said to have a beta distribution with parameters (a, b) if its
probability density function is equal to
f (x) =
1
xa1 (1 x)b1
B(a, b)
0 x 1
and is equal to 0 otherwise. The constant B(a, b) is
Stat 200A Homework 2
(Due Wed. Oct 5 in class)
Note, the Problems and Theoretical Exercises are listed in separate sections at the end of the chapter.
1. Chapter 2, Problem 52
Solution. (a) There are 10
for each pair we can choose either
8 ways to select
16
Chapter 1
Combinatorial Analysis
PROBLEMS
1. (a) How many different 7-place license plates are
possible if the first 2 places are for letters and
the other 5 for numbers?
(b) Repeat part (a) under the assumption that no
letter or number can be repeated
Statistics 206
Homework 1
Due : October 3, 2016, In Class
1. Please tell true or false of the following statements with regard to simple linear regression.
(a) The least squares line always passes the center of the data (X, Y ).
(b) The true regression li
STA 200A: Homework 7
Due Wed. Nov. 9
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 6.P15
Solution:
(a) Let |R| be the area of R.
Z
f (x, y)dxdy = c|R| = 1
R
(b) Let 1
STA 200A: Homework 6
Due: Wed. Nov. 2 in class
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 5.T29
Solution: Let us assume that X has positive pdf over a region (a, b
STA 200A: Homework 6
Due: Wed. Nov. 2 in class
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 5.T29
2. 6.P10
3. 6.P14
1
Stat 200A Homework 1
(Due Wed. Sept 28 in class)
1. Ch. 1, Problem 1
Solution. There are 26 letters and 10 numbers (0-9), which means there are 262 (105 ) = 67, 600, 000.
We need to select 2 numbers in order, of which there are 26(25) outcomes, and 5 lett
STA 200A: Homework 5
Due Wednesday October 26
1. Let X Gamma(, ). Find E[1/X].
2. Let X Uniform[0, 1], and put Y = X. Find E[Y ].
3. Let X be an Exponential() rv. Derive a formula for E[X 2 ].
4. Find the density function of Y = eZ , where Z N (, 2 ). Thi
STA 200A: Homework 4
Due Wednesday October 19
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
h
i
1
.
1. Let X be a Poisson rv with parameter . Calculate E X+1
2. 4.T10
3.
STA 200A: Homework 3
Due Wednesday October 12
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. Three cooks A,B,C, bake a special cake and with probabilities 0.02, 0.03,
STA 200A: Homework 8
Due Wed. Nov. 16
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 6.P54
2. 6.P55
3. 6.T35
4. 7.P4
5. 7.P12
6. 7.P19
7. 7.P30
8. 7.P33
9. Let X and Y
Stat 200A Homework 2
(Due Wed. Oct 5 in class)
Note, the Problems and Theoretical Exercises are listed in separate sections at the end of the chapter.
1. Chapter 2, Problem 52
2. Chapter 2, Theoretical Exercise 11
3. Chapter 2, Theoretical Exercise 20
4.
STA 200A: Homework 7
Due Wed. Nov. 9
Note: Below the notation 3.T11 means Chapter 3, Theoretical Exercise 11. Similarly, the notation 4.P21
means Chapter 4, Problem 21.
1. 6.P15
2. 6.P20
3. 6.P22
4. 6.P44
5. 6.P48
6. 6.T11
7. 6.T25
8. 6.T31
9. Let X and Y
Introduction to Probability and Statistics
Probability & Statistics for Engineers & Scientists, 8th Ed.
2007
Handout #1
Instructor: Kuo-Jung Lee
TA: Brian Shea
The pdf file for this class is available on the class web page.
http:/www.stat.umn.edu/~kjlee/S
Lecture 4/5/16
STS098
Lecture 3
Setwd: set working directory
Getwd: get working directory
Ctab (or you can name it whatever) = table(x$Major, x$Class)
-addmargins(ctab) (this gives sum)list
To make words all lower case: tolower(names(x)
Range: smallest va