STAT/MATH 395 A - PROBABILITY II UW
Spring Quarter 2016
Nhmy Lim
HW5 : Bivariate Distributions (Part 2) Solutions
Problem 1. Let X and Y be two random variables with respective standard
deviations X and Y and with correlation coefficient XY .
(a) Show tha
STAT/MATH 395 A - PROBABILITY II UW
Spring Quarter 2016
Nhmy Lim
HW7 : Distribution of Random Samples & Limit theorems
Solutions
Problem 1. Let X be a continuous random variable on a probability space
(, A, P). For n 1, let (Xn ) and (Yn ) be two sequenc
STAT/MATH 395 A - PROBABILITY II UW
Spring Quarter 2016
Nhmy Lim
HW1 : Continuous Random Variables (Part 1)
Solutions
Problem 1. Let X be a continuous random variable whose probability density
function is:
fX (x) = 3x2 1[0,1] (x)
(a) Verify that fX is a
STAT/MATH 395 A - PROBABILITY II UW
Winter Quarter 2016
Nehemy Lim
HW5 : Bivariate Distributions (Part 2) Solutions
Directions. Show and explain all work to receive full credit. Homework is due on Friday, February 19th at the beginning of class.
Problem 1
STAT/MATH 395 A - PROBABILITY II UW
Winter Quarter 2016
Nehemy Lim
HW3 : Continuous Random Variables (Part 3) /
Moment functions Solutions
Directions. Show and explain all work to receive full credit. Homework is due on Friday, January 29th at the beginni
STAT/MATH 395 A - PROBABILITY II UW
Winter Quarter 2016
Nehemy Lim
HW4 : Bivariate Distributions (Part 1) Solutions
Directions. Show and explain all work to receive full credit. Homework is due on Friday, February 12th at the beginning of class.
The follo
STAT/MATH 395 A - PROBABILITY II UW
Winter Quarter 2016
Nehemy Lim
HW1 : Continuous Random Variables (Part 1)
Solutions
Problem 1. Let X be a continuous random variable whose probability density
function is:
fX (x) = 3x2 1[0,1] (x)
(a) Verify that fX is
STAT/MATH 395 A - PROBABILITY II UW
Winter Quarter 2016
Nehemy Lim
HW7 : Distributions of Functions of Random Variables
Solutions
Directions. Show and explain all work to receive full credit. Homework is due on Friday, March 4th at the beginning of class
STAT/MATH 395 A - PROBABILITY II UW
Winter Quarter 2016
Nehemy Lim
HW2 : Continuous Random Variables (Part 2)
Solutions
Problem 1. Let X follow a standard normal distribution N (0, 1). The probability density function of X is given by :
x2
1
fX (x) = e 2
STAT/MATH 395 A - PROBABILITY II UW
Spring Quarter 2016
Nhmy Lim
HW6 : Bivariate Distributions (Part 3) / Distributions of
Functions of Random Variables Solutions
Problem 1. Consider the set of points G in the two-dimensional plane defined
as :
G = cfw_(x
STAT/MATH 395 A - PROBABILITY II UW
Spring Quarter 2016
Nhmy Lim
HW4 : Bivariate Distributions (Part 1) Solutions
Problem 1. [Ross 6.40.] The joint probability mass function of X and Y is
given by the following table :
X
Y
1
2
1
1
8
1
4
2
1
8
1
2
(a) Give
STAT/MATH 395 A - PROBABILITY II UW
Spring Quarter 2016
Nhmy Lim
HW3 : Moment functions Solutions
Problem 1. Let X be a real-valued random variable on a probability space
(, A, P) with moment generating function MX .
(a) Show that for any constants a, b R
STAT/MATH 395 A - PROBABILITY II UW
Spring Quarter 2016
Nhmy Lim
HW2 : Continuous Random Variables (Part 2)
Solutions
Problem 1. Let Z be a random variable that follows a standard normal distribution N (0, 1). Show that
(a) E[Z] = 0
Answer. The probabili
STAT/MATH 395 A - PROBABILITY II UW
Winter Quarter 2016
Nehemy Lim
HW6 : Bivariate Distributions (Part 3) Solutions
Directions. Show and explain all work to receive full credit. Homework is due on Friday, February 26th at the beginning of class.
Problem 1