Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
Chapter 7: Expected Values of Discrete Random Variables
7
Page 49
Expected Values of Discrete Random Variables
7.1
Expected Value
P
Definition 1. Let X be any random variable over the support RX . Then, whenever xRX xpX (x) <
P
, the expected value of X
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
Chapter 5: Discrete Random Variables and Their Distributions
5
Page 29
Discrete Random Variables and Their Distributions
5.1
Random Variables
Definition 1. A random variable is a realvalued function whose domain is the sample space of a
random experiment
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
Chapter 4: Conditional Probability and Independence
4
Page 19
Conditional Probability and Independence
4.1
Basics
Idea: Suppose there is an experiment in which A and B are two events. Then P r(A) denotes the probability of event A occurring. P r(B) denot
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
Chapter 3: Combinatorial Probability
3
Page 12
Combinatorial Probability
3.1
Basic Counting Rules
Recall the classical probability model (equally likelihood model): in the case of a finite sample space with
equally likely outcomes, we use:
P r(E) =
N (E)
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Solutions to Sample Test #2 (C)
Question 1:
In each case, identify a link between the two families of distributions that are given.
(A) Binomial and Hypergeometric.
So
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Solutions to Sample Test #2 (A)
Question 1:
(A) What is the sample space of this random experiment?
Solution:
= cfw_(1 , 2 ) : 1 1 , 2 7 \ cfw_(6, 6); (7, 7),
where i
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Solutions to Sample Test #2 (B)
Question 1:
(A) What are Bernoulli trials?
Solution: Bernoulli trials are repeated trials of the same random experiment where
1. the ou
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Sample Test #2 (C)
Question 1:
In each case, identify a link between the two families of distributions that are given.
(A) Binomial and Hypergeometric.
(B) Binomial an
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Sample Test #2 (A)
Question 1:
An urn contains 5 red balls (numbered 1 to 5) and 7 blue balls (numbered 1 to 7). Two balls
are to be drawn at random and without replac
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
STAT 2400 Midterm 2 Solutions
1.
a) Let X be the number of criminals he encounters while patrolling in half a day. X P ( = 3.5)
P (X 2) = 1 P (X = 0) P (X = 1) = 1
exp3.5 (3.5)1
exp3.5 (3.5)0
= 0.8641
0!
1!
b) Let Y be the number of criminals he encounte
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Sample Test #2 (B)
Question 1:
(A) What are Bernoulli trials?
(B) Consider a Poisson random variable Y for which
PY (3) = 2PY (2).
What is PY (0)?
(C) Assume that X is
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
Chapters 1 and 2: Basic Concepts
1
Page 1
Basic Concepts
1.1
Set Theory
Definition 1. A set is a collection of distinct elements. If B is a set and b is an element of B, we write
b B; if b is not in B, we write b
/ B. We use cfw_ to denote the empty set
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Solutions to Sample Test #1 (B)
Question 1:
How many different license plates are there when valid license plates are made of
(A) any 3 letters (A to Z) followed by an
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Sample Test #1 (C)
Question 1:
Every morning, in the schoolyard, Ms. Smiths 20 students are lined up before they enter
the school hallway. How many different student l
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability
Solutions to Sample Test #1 (A)
Question 1:
(A) What is the appropriate sample space for this random experiment?
Solution:
= cfw_(i, j) : i, j N, 1 i 6 and 1 j 52.
(B)
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Term Test I Solution Key
Date: Wednesday, February 11, 2015
Duration: 90 minutes
Name:
Student Number:
Instructions
This is a closedbook exam and no notes are allowed
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Solutions to Sample Test #1 (C)
Question 1: (15 marks: 2.5 each)
How many different student lineups are there if
(A) the students are lined up completely at random?
So
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
STAT 2400: Fall 2016
Sample Term Test # 1
Total Marks: 25
Instructions:
 Nonprogrammable and nongraphical calculators are allowed.
 This is a closed book test: no books, notes or formula sheets are allowed.
 Start each question on a new page.
 Show as
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Sample Test #1 (B)
Question 1:
How many different license plates are there when valid license plates are made of
(A) any 3 letters (A to Z) followed by any 3 digits (0
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics ,
STAT 2400
Introduction to Probability I
Midterm 1
CRN: 30357
Instructor: Jenna G. Tichon
Date: Monday, May 25, 2015
Time: 10:45 am to 12:15 pm
Location: 205 Armes
_ Instructions:
All answers must be prope
Université de SaintBoniface (USB) (Affiliated with the University of Manitoba)
Introduction to Probability I
SCIENCE STAT2400

Fall 2015
University of Manitoba
Department of Statistics
STAT 2400
Introduction to Probability I
Sample Test #1 (A)
Question 1:
You are going to first roll a sixsided die, and then draw one card from a regular deck of 52
playing cards.
(A) What is the appropriate