50
60
70 80
90
Solution: use
60 70
80
90
50
70 80
90
Quantiles for tw ins$Sample2
50 60 70 80 90 100
50
70
90
Quantiles for tw ins$Sample1
70
80
90
Logistic QQ - Sample 2
60
60
70
80
90
Weibull QQ - Sample 2
50 60
Q u a n tile s fr o m " lo g is tic " d i
Homework # 8
CDF of X:
Let U=F X ( x )
4 x
F X ( x )=1e
X=
1
log ( 1U ) , where
4
Below if a histogram of generated data:
0 U 1
300
200
0
100
F re q u e n c y
400
500
Generated Exponential(4) Sample,
0.0
0.5
1.0
1.5
2.0
Simulated Observations
Below is Q-Q
Homework #10
Let
f ( y , ) be joint pdf of Y & f ( y , ) is bivariate normal with parameters:
, 2 , , 2 ,
=
Where
COV ( y , )
Var ( y ) Var ( )
From property of bivariate normal distribution, random variable
y
distributed, with the following mean and
Homework # 5
Solution:
1. Shift y variable by 1:
y
f Y ( y )=P ( Y = y ) =(1 p) p
2. Express unknown parameter p as:
q=1 p , then:
1
1
f ( v )= =
= (a q y )
p 1q y=0 y
3. Let:
where:
for
y=0,1,2,3 .
y
f Y ( y )=P ( Y = y ) =(q) (1q)
a y =1 y=0,1,2,3 .
4.
Homework # 6
Problem # 1
a. Create a histogram of Xi + Yi and a histogram of Wi (overlaid on the first histogram). Comment
on your findings. [2 points]
Answer/Discussion:
Since the beta parameter is different for W, the distributions of X+Y is different f
bidders must specify how long the project will take. There will be a significant
penalty for finishing late. One potential contractor determines that the average
time complete a project of this type is 32 weeks with a standard deviation of 7
weeks. The ti
collected from a random sample of SPSS customers asking about their satisfaction
with the software, service, and other features, and some background information
on the customer and their company. 1. One variable in the customer survey asked
about agreemen
a reference list for the citations you use.
Post HIS101 unit 4.1 & 4.2 Discussion latest 2016 august
4.1 Discussion
Debate with your classmates whether the dynastic cycle is unique to China or can
it be connected to other civilizations throughout history.
Make sure to use proper APA format for all citations provided and include a
reference list for the citations you use.
Post HIS101 unit 2 Discussion latest 2016 august
Choose a civilization from ancient China (Shang; Zhou; Han) and one from India
(Harrapan
a PASW Statistics data file from a survey done on the general adult
population. Investigate how the number of siblings (sibs) varies by
highest degree (degree). Ask for appropriate statistics. 2. Is the
assumption of homogeneity of variance met? Is the AN
A game charges $1.00 to play and pays $4.00 if a card drawn from a well shuffld
deck such as above is a face card, other wise the the player loses the money. Find
the expected expected value of the gain for this player.
You may fill the following table to
WITH TWO DECIMALS: Will the Volt be successful or go the way of the
Oldsmobile and the Pontiac? That is the question the CEOs wants you to evaluate
before GM commits funds to design the next generation of Volt and then to
increase its production. Therefor
that the professors response to both questions is yes, find the probability that two of coins
turned up heads?
Last semester in the undergraduate course I was teaching I decided that I would curve the course
and, thus, I had to determine where the break i
the same semester exam in Algebra for so many years that the resulting
distribution for test scores is a normal one. The scores from this years Spring term
have a mean of 74 (out of 100 points) and a standard deviation of 6. The teacher
grades according t
view the distributions of these two variables by gender. Are they similar or
different? Do you see any problems with doing a t test? 2. What do you conclude
about mean differences by gender? 3. Create an error bar chart for each variable by
gender. Is the
to use proper APA format for all citations provided and include a reference list for the citations
you use.
Post HIS101 unit 5 Discussion latest 2016 august
Review and read current events articles from reputable news sources that are highlighting Sunni
an
What is the probability that there will be one defect in a random sample of 24?
What is the probability that there will be less than seven defects in a random
sample of 24? 4. An industrial oven used to cure sand cores for a factory
manufacturing engine b
STAT234: Lecture 5 - Hypothesis Testing
Sabyasachi Chatterjee
Week #5: Page 1 of 38
I
Random Experiment- States, Events
Week #5: Page 2 of 38
I
Random Experiment- States, Events
I
Random Variables - functions on states
Week #5: Page 2 of 38
I
Random Exper
STAT234: Lecture 6 - Confidence Intervals
Sabyasachi Chatterjee
Week #5: Page 1 of 31
A Romantic Experiment !
Week #5: Page 2 of 31
You and your boss !
Week #5: Page 3 of 31
I
Boss: Give me the value of p, the actual proportion of people
leaning right whi
STAT234: Lecture 7 - Type I, Type II and Power
Sabyasachi Chatterjee
Week #5: Page 1 of 23
Last class
Week #5: Page 2 of 23
Last class
I
Type I error : Probability that we reject the null hypothesis
when it is true (fair for statistician)
Week #5: Page 2
STAT234: Lecture 4 - Sums of random Variables
Sabyasachi Chatterjee
Week #5: Page 1 of 33
Binomial Distribution and Normal approx.
More generally if X1 , X2 , , Xn be independent identically
distributed (iid) Ber (p) random variables,
then
Yn =
n
X
Xi Bin
Statistics Help Card
Summary Measures
Sample Mean
x
x1 x2 . xn
n
x
n i
Sample Standard Deviation
( xi x )2
s
n 1
Normal Random Variables
standard score
observation mean x
standard deviation
If X has the N ( , ) distribution, then the random variable