Stat 510 : Test 1.
Moulinath Banerjee
October 21, 2015
Announcement: The homework carries a total of 60 (15 4) points. Extra sheets must
be stapled at the back. Show ALL your work. No calculators allowed. Internet connections on
electronic devices being u

STATS 510 - HW2 Solution
2.4. (a)
+1
Z
f (x)dx =
Z0
1
e x dx +
2
=
+1
Z
1
e
2
=
+1
Z
e
1
1
Z1
=
= 1.
x
dx
0
x
dx +
0
0
1
e
2
h
Z1
1
e
2
x
dx
0
x
x
e
dx
i1
0
(b) For t 0 we have
P(X < t) =
Zt
f (x)dx =
Z0
1
e x dx +
2
1
Zt
1
1 h x it
e x dx =
e
2
2
Zt
1
e

Test 1 Solution
Jinqi Shen
October 17, 2016
Remark This solution has been proofread carefully and if you find mistakes,
please email the GSI for editing it.
Question 1
Without loss of generality, we can assume that the candies in the right pocket
are blue

Chapter 1 Probability
1.1 Sample space and events (CB 1.1)
An experiment is any action or process by which observations are generated.
Examples include:
tossing a coin
rolling a die
buying a lottery ticket
taking a course in statistics
trying a new medica

Chapter 4 Multiple Random Variables
4.1 Joint and marginal distributions (CB 4.1)
Let X, Y be two rvs defined on the sample space of an experiment. (X, Y )
is said to be a random vector (r.v.). If both X, Y are discrete, the joint probability mass functio

Chapter 2 Transformations and Expectations
2.1 Distributions of functions of a random variable (CB 2.1)
Let X be a r.v. whose distribution is given. In this section we are interested
in methods for finding the distribution of Y := g(X) for some function g

Chapter 3 Common Families of Distributions
3.1 Discrete distributions (CB 3.2)
Binomial distribution
An experiment which satisfies the following conditions 1-4 is called a binomial
experiment:
(a) The experiment consists of a sequence of n trials where n

Homework 1 Solution
Jinqi Shen
September 29, 2016
1.19
(a)For every possible partial derivative of the form
4 f (x,y)
k
k
k
x1 1 x2 2 x3 3
, we only
need the following two conditions hold
k1 0, k2 0, k3 0
k1 + k2 + k3 = 4.
are
This
is equivalent to plac

Homework 2
Moulinath Banerjee
University of Michigan
September 30, 2016
Problem 1: A line is drawn through a point (-1,0) in a random direction. Let (0, Y )
denote the point at which it cuts the Y -axis. Find the (p.d.f) density of Y .
Problem 2: Let W be

Homework 1: Stat 510
Moulinath Banerjee
September 15, 2016
(1) Problems from CB: 1.36, 1.39, 1.46. 1.51, 1.19. 1.21, 1.24, 1.31 (a) and (c).
Comments: For 1.31 you may assume that if w1 , w2 , . . . , wn are integers summing
P
up to n, then the weighted a

Problem Set 1
Stats 510 Fall 2016
Due Wednesday, September 21 in class
Instructions. Do all problems and you must show your work. You may work in teams, but
you must write out your own homework solutions. Please make sure your participation is a
two-way s

Problem Set 2
Stats 510 Fall 2016
Due Wednesday, September 28 in class
Instructions. Do all problems and you must show your work. You may work in teams, but
you must write out your own homework solutions. Please make sure your participation is a
two-way s

Problem Set 1 - Solutions
Stats 510 Fall 2016
Instructions. Do all problems and you must show your work. You may work in teams, but
you must write out your own homework solutions. Please make sure your participation is a
two-way street and make sure that