Quiz Submissions - Midterm Exam Review
Victoria Grant (username: vgrant3)
Attempt 4
Written: Mar 4, 2016 8:28 PM - Mar 5, 2016 8:55 AM
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ProbTabl
e
Question 1
1/1
point
Provide an appropriate respon
Lect 18
Anh Phung
March 2016
1
Hypothesis Testing (Ch 8)
Decided between two competing claims about the population, based on observing only a sample from the population.
Reject H0 (conclude HA ) only if sufficiently strong evidence against H0 (in favor
of
Lect 23
Anh Phung
April 2016
1
Conditional Probability - Sec 2.4
Def: Given two events A and B, the conditional probability B given A is
P (B | A) =
P (AB)
P (A)
Ex: Alcohol use, 348 male students cross-classified by age group (18-20,2123,24+) and episode
Lect 21
Anh Phung
April 2016
1
Midterm 2
Secs 5.3-5.4, 6.1-6.2, 7.1-7.3, 8.1-8.4
There may be TF/MC.
There will be problems. There will not be problems drawn from Chapter 6.
Two important ideas from Chapter 6:
=
1. Unbiasedness: E()
In many many samples,
Lect 26
Anh Phung
April 2016
1
Announcements
Final exam is Thu May 12 4pm.
Review is Thu May 5 11:40-12:55 and 4:10-5:25
Final exam (Sections in text)
Chs 1-2, 3.1-3.4, 4.1-4.3, Chs 5-6, 7.1-7.3, 8.1-8.4, 9.1-9.4, Ch 12
There will be questions on conditio
Lect 25
Anh Phung
April 2016
1
Announcements
Final exam Thu May 12, 4pm
Thu May 5 Review session. 11:40 - 12:55 or 4:10-5:25
2
Continued
Ex: X and Y are continuous rvs with joint density
(
k(x2 + y 2 ) 0 < x < 9, 0 < y < 9
f (x, y) =
0
otherwise
Whats k?
Lect 24
Anh Phung
April 2016
1
Conditional Probability
Ex: Our baseball team plays 20% of games against LHP, and 80% against RHP.
Against LHP we win 40% of games, against RHP we win 70% of games.
(Overall we win 64% of games)
We have a game today. The pro
Statistics 2000 Spring 2008
Midterm Exam 1
March 12, 2008
Name (2 points):
Instructions: There are 50 points total. Read each part of each question carefully. You are
responsible for checking that your exam is complete. You are permitted one (two-sided) s
Probability and Statistics (UN1201)
Fall 2016
https:/courseworks.columbia.edu
John P. Cunningham
jpc2181@columbia.edu
Ian Kinsella
iak2119@columbia.edu
MIDTERM EXAM
Total time: 75 minutes. To be taken in-class, Monday 24 October 2016.
Do not open this exa
Course: STAT UN1201
Title: Probability and Statistics
Semester: Fall 2016
Instructor: John P. Cunningham
PRACTICE EXAM PROBLEMS
Notes:
These problems are (much) more numerous than you should expect to see on the exam.
These problems are given in additio
Lect 11
Anh Phung
February 26, 2016
1
Introduction
Consider a large population and numerical variable. (Height in inches of US
adult males) (Suppose population mean is , population SD is ).
Imagine we take a random sample of n, sample mean x. Take another
Lect 19
Anh Phung
March 2016
1
Hypothesis Testing - Ch8
1. State H0 and HA (we will assess evidence against H0 , in favor of HA ) (either
reject or fail to reject H0 ).
2. Compute a measure of disagreement between data observed and what wed
expect if H0 w
Lect 7
Anh Phung
February 11, 2016
1
Chapter 3
Ex: X number of times order messed up in 4 days, prob for each day is .30
X Binomial(n = 4, p = .30)
x
0
1
2
3
4
p(x)
.24
.41
.26
.08
.01
General form of probs for X Binomial(n, p)
p(x) = P (X = x) = px (1 p)
Lect 9
Anh Phung
February 21, 2016
1
Normal Distribution
Def: The rv X has a normal dist with parameters and id its pdf is
f (x; , ) =
1
2
1
e 22 (x)
2
Write X N (, 2 )
Properties of the Normal Dist:
Density is unimodal (at ), symmetric (about ), bell-
Lect 20
Anh Phung
April 2016
1
Chapter 9
Ex: It is claimed that the average score on an exam is 500. We believe its
lower. We test 475 students, get mean score of 485 and standard deviation of
90. Do the data confirm our suspicion?
(z =
485500
90
475
= 3.
Lect 14
Anh Phung
March 2016
1
Section 6.2
Maximum likelihood estimation
Ex: Ch6 Exercise 20
X Binomial(n = 20, p =?). Find the MLE of p.
Observe X = x = 3. Should get .15?
p(x; ) = nx x (1 )nx
L(; x) = nx x (1 )nx
(notation alert, switch back to p)
ln L(
Lect 13
Anh Phung
March 2016
1
Chapter 6
Ex1: Whats the average HS GPA of Columbia UGs?
Sample 100 students.
Ex2: What percentage of NYers would vote Clinton over Rubio?
Sample 200 voters.
Def: A statistic is any quantity that can be calculated from data.
Lect 10
Anh Phung
February 21, 2016
1
Normal Distribution
If X1 N (1 , 12 ), X2 N (2 , 22 ) and X1 , X2 are independent, then
X1 + X2 N (1 + 2 , 12 + 22 )
and
X1 X2 = N (1 2 , 12 + 22 )
More generally (Sec 5.5), if X1 , X2 , ., Xn are indep rvs, with E(Xi
Lect 17
Anh Phung
March 2016
1
Section 7.3
We have three formulas for 100(1 )% CI for
X z 2 n (exact of population Normal otherwuse approx if n is large, assume
is known)
X z 2 sn (only approx, only works if n large)
X t 2 ,n1 sn (exact assuming Normal
Lect 8
Anh Phung
February 16, 2016
1
Examples
1. Chapter 4 Exercise
5
kx2 if 0 x 2
Let X has pdf f(x) =
0
else
Find P (X 1), P (1 X 1.5), P (X > 1.5).
Solution:
R
To find k, set
Z
f (x)dx = 1, solve for k.
Z
f (x)dx =
2
kx2 dx =
0
To find
the cdf of X:
Lect 16
Anh Phung
March 2016
1
Example
Ex: Test scores follow Normal dist, mean is , unknown SD is = 100. Random
sample of n = 475 students, average score was X = 485.
A 99% CI for the true mean score (avg of all students) is X + z 2 n or
[473.2,496.8]
Th
Lect 15
Anh Phung
March 2016
1
Confidence Interval
Ex: Test scores follow Normal dist with unknown mean and known SD
= 100. We test 475 students, get average scores of x = 485.
2
=
Observe value x = 485 is a realization of the rv X, X N (X = , X
2
n
=
21
Lect 12
Anh Phung
February 2016
1
Midterm
MT1 is Tue March 1. Allowed calculator and one 8.5 by 11 sheet (both sides)
of original handwritten notes.
HW 1-3. Lecture to the line (2/18).
Text: 1.1 1.4, 2.1 2.31 , 2.52 , 3.1 3.4, 3.53 , 4.1 4.3, 5.54
1. Basi