Introduction to Probability and Statistics with
Calculus (UN1201)
Fall 2016
https:/courseworks.columbia.edu
John P. Cunningham
[email protected]
stat.columbia.edu/%7Ecunningham
Course Syllabus
Description
This course provides a comprehensive introducti
STAT UN1201 (002)
Prof. Joyce Robbins
January 24, 2017
Course Materials
https:/github.com/jtr13/1201
Textbook
Help Room
http:/stat.columbia.edu/help-room/
Probability
In 1654, writer Antoine Gombaud Chevalier de Mr wants to know if the following
bets are
STAT UN1201
March 28, 2017
(8.4, 8.5, 9.1)
1
Proportions, Large Sample (8.4)
Ho: p = po
Test statistic =
#$%#&
#& (%#& )/+
HA: p > po, p < po, or p po
(npo 10 and n(1- po) 10)
2
Proportions, Small Sample (8.4)
STAT UN1201
March 21, 2017
(parts of 8.1 8.5)
updates after class in red
1
Hypothesis Testing
p. 333 #19a
The melting point of each of 16 samples of a certain brand of
hydrogenated vegetable oil was determined, resulting i
STAT UN1201
March 23, 2017
(Review + parts of 8.1 8.5)
1
5.3 Statistics and Their Distributions
Population
n = 3
N = 31
Samples
2
Sample Means
> mean(rnorm(100, mean = 50, sd = 10)
[1] 52.55979
> mean(rnorm(100, mean = 50, sd = 10)
[1] 50
Chapter 3: Discrete Random Variables and Probability Distributions
e.
49.
With n = 50, P(X = 0) =
50
0
(.05)0 (.95)50
(.95)50 = .077.
Let X be the number of seconds, so X ~ Bin(6, .10).
n x
6
p (1 p ) n x =
(.1)1 (.9) 5 .3543 .
a. P(X = 1) =
x
1
b.
P(X
6
UN1201 HW2 Solution
3.10. The number of pumps in use at both a six-pump station and a four-pump
station will be determined. Give the possible values for each of the following
random variables:
a. T = the total number of pumps in use
b. X = the differ
Homework 1 Solution
Shuaiwen Wang
Problem 12
Solution: As we can see in Figure 1 the values concentrates around 0.4.
Figure 1: The stem-and-leaf plot of the data.
Problem 25
Solution: As we can see in Figure 2, the logarithm transformation decreases the l
Displaying and Describing Quantitative
Data
1.2 Histograms in Descriptive Statistics, 1.3 Measures of
Location, 1.4 Measures of Variability
Thought Question
1. If you were to read the results of a study showing
that daily use of a certain exercise machine
Keep In Touch?
Examining how Columbia affects our Connections with Family and
High School Friends
Laurice Wong
Statistics 1201
Professor Anthony Donoghue
Survey Project, Part I
17th November, 2016
1 of 16
PART 1
1. Purpose of the Survey
As an undergraduat
STAT 1201 Project Part 2 | Laurice Wong (lw2646)
PART II
1.
LINEAR REGRESSION ANALYSIS
Question: Is there a relationship between the number of classes taken and the number of
extracurricular clubs involved in during the semester?
PART A: LINEAR REGRESSIO
STAT UN1201
March 2, 2017
1
Review: Point Estimation (6.1)
If an estimator, ", is unbiased, E(") =
$) = long run average, sometimes above,
ex. E(X
sometimes below the actual parameter
ex. E(S2) = 2
,
*
('
)'
)
(
.
S2 =
/
STAT UN1201
March 9, 2017
(parts of 7.3, 8.1, 8.2, 8.3)
1
7.3 CI for Means, small n, unknown
(
%/'
)
only for large n (> 40)
for smaller n, this underestimates the true confidence
interval, therefore, we substitu
STAT UN1201
February 28, 2017
2/28/17
1
Distribution of the Sample Mean (5.4)
# = &# =
# =
)
&#
)
=
&# =
(standard error
of the mean)
mean of sample means =
mean of population
2
Distribution of the Sample Total
- = . + ) + +
STAT UN1201
February 7, 2017
Negative Binomial
A coin is flipped until you get 3 tails
X = number of heads
What is P(X = 5)?
(total flips 3)
Negative Binomial
A weighted coin is flipped until you get 3 tails
X = number
STAT UN1201
February 9, 2017
February 14, 2017
2/15/17
1
f(x) =
probability
density
function
f(x)
graph of f(x) =
density curve
a
b
,
= (
2/15/17
(area under the curve between a and b)
2
4.2 Cumulative Distribution Function
STAT UN1201
February 2, 2017
3.4 The Binomial Probability Distribution
1. n trials
2. each trial has only 2 outcomes (S or F)
3. trials are independent
4. probability of success P(S) is constant, called p
Independence and