Stat 4201, Spring 2015: HW 5
This homework is due on Friday February 20. You are encouraged to talk with each other and
get help. However, you should understand everything that you write, as there will be a quiz during
lecture on the due date, which will
Stat 4201, Spring 2014: HW 5 Solutions
This homework is due on Wednesday February 19. You are encouraged to talk with each other
and get help. However, you should understand everything that you write, as there will be a quiz
during lecture on the due date
Stat 4201, Spring 2015: HW 5 Solutions
In the 8th edition of the textbook do exercises: 3.74, [with reference to 3.42 and 3.70, nd Cov(X, Y )],
4.47, 4.49, 4.50, 4.58, 4.64, 4.80
In the 7th edition, these are: 3.74, 4.42, 4.46, 4.48, 4.49, 4.57, 4.62, 4.7
Stat 4201 Autumn 2013
Midterm 1
Name:_
1) The probability density function of a random variable is given by
,
0>
= 50
0,
0
a. (7 pts) Find the cumulative distribution function .
b. (6 pts) Use your answer from part (a) to find > 15
c. (6 pts) Find >
Stat 4201, Spring 2015: HW 1
This homework is due on Wednesday January 21. You are encouraged to talk with each other
and get help. However, you should understand everything that you write, as there will be a quiz
during lecture on the due date, which wil
Stat 4201, Spring 2014: HW 6
This homework is due on Wednesday February 26. You are encouraged to talk with each other
and get help. However, you should understand everything that you write, as there will be a quiz
during lecture on the due date, which wi
Stat 4201 Autumn 2013
Midterm 2
Name:_
Recitation (circle one): 11:30a 12:40p
General instructions:
Show all supporting work to justify your answer. If you use a built-in function on your
calculator, write down the name of the function used with the value
Stat 4201, Spring 2015: HW 6
This homework is due on Wednesday February 25. You are encouraged to talk with each other
and get help. However, you should understand everything that you write, as there will be a quiz
during lecture on the due date, which wi
Stat 4201, Spring 2015: HW 6
In the 8th edition of the textbook do exercises: 5.16, 5.17, 5.23, 5.24, 5.40, 5.41, 5.51
In the 7th edition, these are: 5.16, 5.17, 5.23, 5.24, 5.40, 5.41, 5.51
5.16 If X Negative Binomial(k, ), then, in the books notation, P
Stat 4201, Spring 2015: HW 4
This homework is due on Wednesday February 11. You are encouraged to talk with each other
and get help. There will be NO quiz during lecture on the due date for this home. Instead, we will
have the rst midterm exam on Wednesda
Stat 4201
Lecture 18
Poisson Distribution and Multinomial Distribution
When n is large, calculating binomial probabilities can be tedious. A limiting form of the
binomial distribution when n , 0 while n remains constant can be used to find
probabilities.
Stat 4201
Lecture 21
Chi Square, Beta, and Weibull Distributions
In the last lecture, we learned the Exponential Distribution was a special case of the Gamma
Distribution where 1 and . We now turn to another special case of the Gamma
Distribution called t
STAT 4201, Spring 2017: Homework 8
This homework is due on Wednesday March 29 and will be graded by Natalia Kravtsova.
Submit this homework to the TA at the recitation you registered. Do not submit the
homework to the professor. You are encouraged to disc
STAT 4201, Spring 2017: Homework 9
This homework is due on Wednesday April 5 and will be graded by Guowei Li. Submit this
homework to the TA at the recitation you registered. Do not submit the homework
to the professor. You are encouraged to discuss with
Normal Distribution
Probability density function for a normal random variable.
Normal Distribution
The density function of the normal random variable X , with mean
and variance 2 > 0, is
(x )2
1
exp
f (x) =
, < x < .
2 2
2
E(X ) = ,
and
Var(X ) = 2 .
S
Stat 4201
Lecture 15
The Binomial Distribution
Last time we discussed the Bernoulli distribution, which is in some sense the simplest discrete
distribution: that of one trial involving either success (X=1) or failure (X=0).
Of course, repeated trials are
Stat 4201
Lecture 13
Conditional expectations
In the last lesson, we learned how to find the mean and variance of linear combinations of
random variables. We also learned how to find the covariance between two linear combinations
of random variables.
We s
Stat 4201
Lecture 22
Pareto and Normal Distributions
Pareto Distribution
Definition A random variable X has a Pareto distribution if and only if its probability density
for x > 1 and 0 elsewhere. 0
x 1
The Pareto distribution is sometimes expressed more s
Stat 4201
Lecture 19
Continuous Density Functions, Uniform Distribution
In Chapter 5, we covered the most common discrete distributions that arise in real-life
applications. We now turn to some prominent continuous densities that occur in statistical
theo
Stat 4201
Lecture 20
Gamma and Exponential Distributions
In the last lecture, we discussed the Uniform Distribution. We noticed that the function gave the
height of the curve, and not the probability of a specific value of the random variable X. Thus,
the
Stat 4201
Lecture 14 Add-on
Discrete Uniform Distribution
Example: If X has the discrete uniform distribution () =
1
for = 1,2, , , show that its moment-
generating function is given by
() =
(1 )
(1 )
We use the geometric sum formula (again):
Thus,
Exam
Stat 4201
Lecture 12
Moments of Linear Combinations of Random Variables
Beginning of Midterm 2 Material
One more comment on moment-generating functions. Interesting tie between momentgenerating functions and Maclaurins series:
Maclaurins series expansion
Stat 4201
Lecture 17
Hypergeometric Distribution
To obtain a formula analogous to that of the binomial distribution that applies to sampling
without replacement, in which case the trials are not independent, we consider the following
scenario:
A set of N
Stat 4201
Autumn 2016
Quiz 1 Sep/20/2016
Time Limit: 25 Minutes
Name (Print):
Name.number :
Time (circle):
Teaching Assistant:
8:00 am, 11:30 am, 12:40 pm
Jiae Kim
This quiz contains 4 problems. Check to see if any pages are missing.
You may not use your
Stat 4201
Autumn 2016
Quiz 2 Oct/11/2016
Time Limit: 25 Minutes
Name (Print):
Name.number :
Time (circle):
Teaching Assistant:
8:00 am, 11:30 am, 12:40 pm
Jiae Kim
This quiz contains 2 problems. Check to see if any pages are missing.
You may not use your
Stat 4201
Autumn 2016
Quiz 3 Oct/25/2016
Time Limit: 25 Minutes
Name (Print):
Name.number :
Time (circle):
Teaching Assistant:
8:00 am, 11:30 am, 12:40 pm
Jiae Kim
This quiz contains 2 problems. Check to see if any pages are missing.
You may not use your
Homework 2
Stat 4201
Fall 2016
Name:
Recitation time:
Please write down your name and recitation time (8:00, 11:30 or 12:40) above.
This homework contains 13 pages (including this cover page) and 7 questions. Make
sure you have them all.
Justify your a
Stat 4201
Autumn 2016
Quiz 4 Nov/15/2016
Time Limit: 25 Minutes
Name (Print):
Name.number :
Time (circle):
Teaching Assistant:
8:00 am, 11:30 am, 12:40 pm
Jiae Kim
This quiz contains 2 problems. Check to see if any pages are missing.
You may not use your
Random Variable Transformations
Transformation of random variables: problem statement
Given one random variable X , we may be interested in finding the
distribution of
Y = g (X )
for some function g ().
Given several random variables X1 , . . . , Xn , we
Chapter 8
Sampling Distributions
Definition: Population
Population. A set of numbers from which a sample is drawn is
referred to as a population. The distribution of the numbers
constituting a population is called the population distribution
Definition: R
April 28, 2017
Final Exam
STAT 4201
Final Exam Solution
Global rules: if two different results are given to one question, they will be both graded as wrong
answers regardless of their correctness per se. If a correct final result is given but the supporti
March 10, 2017
Midterm Exam 2
STAT 4201
Midterm Exam 2
Do not open this test booklet until you are directed to do so.
You will have 55 minutes to complete the exam. There are 4 questions.
This is a closed book exam. You may use a calculator and two dou