Statistical and Mathematical Methods DS-GA 1002
November 16, 2016
Homework 9
Due Sunday, November 27
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1. Empirical probability mass function. Y
Statistical and Mathematical Methods DS-GA 1002
September 14, 2016
Homework 1
Due Wednesday, September 21
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1. True or False. Prove the following statements o
Statistical and Mathematical Methods DS-GA 1002
November 25, 2016
Homework 10
Due Friday, December 2
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1. Sign test. Your friend is convinced th
Statistical and Mathematical Methods DS-GA 1002
October 26, 2016
Homework 6
Due Friday, November 4
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1. Radioactive sample. Consider the followi
Statistical and Mathematical Methods DS-GA 1002
November 9, 2016
Homework 8
Due Friday, November 18
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1. Descriptive statistics. Find a dataset
Statistical and Mathematical Methods DS-GA 1002
November 2, 2016
Homework 7
Due Friday, November 11
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1. Rejection sampling for discrete data. I
Statistical and Mathematical Methods DS-GA 1002
October 19, 2016
Homework 5
Due Friday, October 28
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1. Basketball. A data analyst working for t
DS-GA 1002 Lecture notes 7
November 9, 2015
Statistics: Estimation
Estimation is a classical problem in statistics. We have access to samples from a random
vector Y and want to estimate the correspond
DS-GA 1002 Lecture notes 2
September 21, 2015
Probability (continued)
1
Random variables (continued)
1.1
Conditioning on an event
Given a random variable X with a certain distribution, imagine that it
Statistical and Mathematical Methods DS-GA 1002
December 9, 2015
Homework 11 Solutions
1. (10 points) Convexity (10 points).
a. For any 0 1 and any x, y R,
f (x + (1 ) y) =
n
X
i=1
n
X
ai fi (x + (1 )
Statistical and Mathematical Methods DS-GA 1002
December 16, 2015
Final Solutions
1. Short questions (20 points)
a. Any vector in span cfw_u1 , u2 can be written as x := u1 + u2 for some , R. By
line
DS-GA 1002 Lecture notes 5
October 19, 2015
Statistics: Learning models from data
Learning models from data that are assumed to be generated probabilistically from a certain
unknown distribution is a
DS-GA 1002 Lecture notes 1
September 14, 2015
Probability
1
Introduction
Probability theory is a tool that allows us to reason mathematically about uncertainty. In
this notes we will learn how to buil
DS-GA 1002 Lecture notes 0
September 14, 2015
Set theory
1
Basic definitions
A set is a collection of objects. The set of all elements that we consider in a certain situation
is called the universe an
DS-GA 1002 Lecture notes 6
November 2, 2015
Statistics: Hypothesis testing
1
The hypothesis testing framework
In a medical study we observe that 10% of the women and 12.5% of the men suffer from
heart
Statistical and Mathematical Methods DS-GA 1002
November 2, 2015
Homework 7
Due Tuesday, November 10
Please either give the assignment to Loraine at the CDS or send it via email
to the graders before
Statistical and Mathematical Methods DS-GA 1002
November 5, 2015
Homework 6 Solutions
1. (10 points) Uniform distribution.
a. u has to be larger than x(n) = maxcfw_x1 , x2 , . . . , xn .
b. The likeli
Statistical and Mathematical Methods DS-GA 1002
November 11, 2015
Homework 7 Solutions
1. (10 points) Short questions.
a. No. In fact, it can still be quite clear that it doesnt hold, but we cannot ru
Statistical and Mathematical Methods DS-GA 1002
November 11, 2015
Homework 8
Due Tuesday, November 17
Please either give the assignment to Loraine at the CDS or send it via email
to the graders before
Statistical and Mathematical Methods DS-GA 1002
November 16, 2015
Homework 9
Due Tuesday, November 24
Please either give the assignment to Loraine at the CDS or send it via email
to the graders before
Statistical and Mathematical Methods DS-GA 1002
November 23, 2015
Homework 10
Due Tuesday, December 8
Please either give the assignment to Loraine at the CDS or send it via email
to the graders before
Statistical and Mathematical Methods DS-GA 1002
November 17, 2015
Homework 8 Solutions
1. (10 points) Probability of error vs MSE (10 points).
a. We can easily find the piecewise constant density of Y
Statistical and Mathematical Methods DS-GA 1002
November 25, 2015
Homework 9 Solutions
1. (15 points) Projections.
a. False. This only holds if the vectors in the basis are orthogonal. Take
0
1
b=
Statistical and Mathematical Methods DS-GA 1002
December 6, 2015
Sample Final Problems
1. Short questions
a. For a m n matrix A with rank n, where m > n, is it possible for Ax = b to have no
solution?
Statistical and Mathematical Methods DS-GA 1002
December 8, 2015
Sample Final Problems Solutions
1. Short questions
a. Ax = b has a solution if b is in the range of A. The dimension of the range of A
Statistical and Mathematical Methods DS-GA 1002
October 27, 2015
Homework 6
Due Tuesday, November 3
Please either give the assignment to Loraine at the CDS or send it via email
to the graders before n
Statistical and Mathematical Methods DS-GA 1002
December 14, 2015
Final
The duration of the exam is 3 hours.
The exam is open book. You may use electronic devices but only to view the lecture
notes.
DS-GA 1002 Lecture notes 10
November 23, 2015
Linear models
1
Linear functions
A linear model encodes the assumption that two quantities are linearly related. Mathematically, this is characterized usi
DS-GA 1002 Lecture notes 9
November 16, 2015
Linear models
1
Projections
The projection of a vector x onto a subspace S is the vector in S that is closest to x. In
order to define this rigorously, we
DS-GA 1002 Lecture notes 8
November 9, 2015
Linear models: Algebra
Linear models are a pillar of modern data analysis. Many phenomena can be modeled as
linear, at least approximately. In addition, lin