FSRM 582, Homework 3
Assigned: September 23, 2015
Due: September 29, 2015
Problem 1. Let A1 , A2 , . . . , An be independent events and dene the indicator functions
Ij () =
1
0
if Aj ,
if Aj ,
/
for and j = 1, 2, . . . , n. Aditionally, for j = 1, . . . ,

Rutgers Business School
Fall 2016
Introduction to Probability: Solutions to Homework 1
Problem 1.
The probability pn that in a room of n people they all have different birthdays is
364
363
362
365 n + 1
pn =
,
365
365
365
365
for n = 1, 2, . . . , 365.
Th

Rutgers Business School
Fall 2016
Introduction to Probability: Homework 3
Homework to be handed in at the beginning of the next class (Wednesday September 28th, 10am).
Explain all your answers and show your working.
Problem 1.
(i) If A, B and C are three

Rutgers Business School
Fall 2016
Introduction to Probability: Homework 1
Homework to be handed in at the beginning of the next class (Wednesday September 14th, 10am).
Explain all your answers and show your working.
Problem 1. How many people would you ne

Rutgers Business School
Fall 2016
Introduction to Probability: Solutions to Homework 2
Problem 1. One way to do this is to calculate the number of meals with j cheese courses for j = 1, 2, 3 and sum
them to find the total number of meals with a cheese cou

Rutgers Business School
Fall 2016
Introduction to Probability: Solutions 4
Problem 1. There are several equivalent ways to do this. From first principles, we have
P (E c F c ) = P (F c ) P (E F c ) (since F c can be written as the disjoint union of E F c

Rutgers Business School
Fall 2016
Introduction to Probability: Solutions 3
Problem 1.
(i) By the inclusion-exclusion principle,
P (A B C) = P (A) + P (B) + P (C) P (B C) P (C A) P (A B) + P (A B C) so
P (A B C) P (A) = P (B) + P (C) P (B C) P (C A) P (A B

Rutgers Business School
Fall 2016
Introduction to Probability: Homework 7
Homework to be submitted on Blackboard by 10am on Wednesday November 9th.
Please ensure your homework is a pdf or word doc.
Explain all your answers and show your working.
Problem 1

Rutgers Business School
Fall 2016
Introduction to Probability: Solutions 6
Problem 1. Let X be the number of accidents in the next month, then X is Poisson with parameter = 3.5/12 =
7/24.
(i) We wish to calculate the probability X is at least 2, which is

Rutgers Business School
Fall 2016
Introduction to Probability: Homework 6
Homework to be submitted on blackboard by 10am on Wednesday October 19th.
Please ensure your homework is a pdf or word doc.
Explain all your answers and show your working.
Problem 1

Rutgers Business School
Fall 2016
Introduction to Probability: Homework 5
Problem 1. Let X Bi(10, 1/2) and Y Bi(20, 1/2).
We need to check which is bigger, P (X = 5) or P (Y = 10). We have
10
20
P (X = 5) =
(1/2)5 (1/2)5 and P (Y = 10) =
(1/2)10 (1/2)

Rutgers Business School
Fall 2016
Introduction to Probability: Homework 4
Homework to be submitted on Blackboard before Wednesday October 5th, 10am.
Explain all your answers and show your working.
Problem 1. Show that if the events E and F are independent

FSRM 582
Introduction to Methods and Theory of
Probability
with Financial Applications
Fall 2015
Instructor: Lee Dicker
Notes 1
About this course
What is the dierence between probability and statistics?
Probability models
Probability
Statistics
Deduction

FSRM 582
Introduction to Methods and Theory of
Probability
with Financial Applications
Fall 2015
Instructor: Lee Dicker
Notes 2
Discrete random variables
Denitions
A discrete random variable may take only countably many
possible values. (i.e., R is a coun

16:960:581
Homework 7
Due November 9th 2016, 6:40pm
Notes. NO late submission will be accepted, except under special circumstances. All homework assignment must be written on standard 8.5 by 11 paper and stapled together. Computer generated output
without

16:960:581
Homework 5
Due October 12 2016, 6:40pm
Notes. NO late submission will be accepted, except under special circumstances. All homework assignment must be written on standard 8.5 by 11 paper and stapled together. Computer generated output
without d

16:960:581
Homework 6
Due November 2nd 2016, 6:40pm
Notes. NO late submission will be accepted, except under special circumstances. All homework assignment must be written on standard 8.5 by 11 paper and stapled together. Computer generated output
without

16:960:581
Homework 4
Due October 5 2016, 6:40pm
Notes. NO late submission will be accepted, except under special circumstances. All homework assignment must be written on standard 8.5 by 11 paper and stapled together. Computer generated output
without de

16:960:581
Homework 2
I
Due September 21 2016, 6:40pm
Notes. NO late submission will be accepted, except under special circumstances. All homework assignment must be written on standard 8.5 by 11 paper and stapled together. Computer generated output
witho

Rutgers Business School
Fall 2016
Introduction to Probability: Homework 2
Homework to be handed in at the beginning of the next class (Wednesday September 21st, 10am).
Explain all your answers and show your working.
Problem 1. A menu has 5 starters, 7 mai

Rutgers Business School
Fall 2016
Introduction to Probability
26:960:575
Place:
Time:
Instructor:
Office:
E-Mail:
Office Hours:
1 Washington Place, Room 512, Newark, NJ 07102
Wednesdays 10:00-12:50
Thomas Lidbetter
1 Washington Place, Room 1076, Newark, N