Statistics 321 (L01): Notes and Class Examples of May 15
Prior to introducing the notion of probability, there are some terms that need to be defined. These are:
1. random experiment
2. sample space, or (S)
3. event.
Definition: A random experiment is a p

Statistics 321 Lab #5: Continuous Random Variables. Uniform and Normal
Distributions.
Working with Probability Density functions (f (x)s) and Cumulative Distribution Functions (F (x)s)
Lab Exercise 1. A random variable X has the probability density functi

Chapter 2: Probability
2.1
A = cfw_FF, B = cfw_MM, C = cfw_MF, FM, MM. Then, AB = 0/ , BC = cfw_MM, C B =
cfw_MF, FM, A B =cfw_FF,MM, A C = S, B C = C.
2.2
a. AB
b. A B
d. ( A B ) ( A B )
c. A B
2.3
2.4
a.
b.
8
Chapter 2: Probability
9
Instructors Solutio

Statistics 321 (Spring 2015): Bivariate Probability Distributions - Independent
Random Variables
Definition: Let X and Y be two random variables having a joint cumulative probability distribution function
F (x, y). X and Y are said to be independent rando

Statistics 321 (Spring 2015): The Gamma Distribution and its Special Cases
The Gamma Function
Definition: The following is called the Gamma Function:
Z
xk1 ex dx
(k) =
0
Properties of the Gamma Function
1. (k) = (k 1)! for k is an integer.
2. (k + 1) = k

Statistics 321 (Spring 2015) Lab #1: Counting Methods and Probability More Practice
In todays lab, complete the following:
1. Lab Exercise 1
2. Lab Exercise 2
3. Lab Exercise 3
4. Lab Exercises 4
Lab Exercises 5 and 6 after Fridays lecture, as there are a

Statistics 321 (Spring 2015) Lab #2: Counting Methods and Probability More Practice
Here are some more practice problems that cover the counting methods covered in Fridays lecture.
1. A recent shipment of 40 vehicles was received at a local car dealership

Statistics 321 (L01) - The Law of Total Probability and Bayes Theorem
Result: (Law of Total Probability) Let B1 , B2 , , Bk represent events that are pairwise mutually
exclusive, meaning Bi Bj = for all i 6= j. Let A represent some other event, which is c

Statistics 321 (Spring 2015): An Introduction to Bivariate Probability
Distributions
Bivariate probability distributions describe the co-behaviour of two random variables. Some examples include
Ex.1 - Randomly pick three cards from a deck and observe two

Statistics 321 (Spring 2015): More Discrete Probability Distributions - The
Poisson and Hypergeometric Distributions
The Poisson Distribution
Definition: A random variable X is said to follow a Poisson distribution if and only if the probability
distribut

Stat 321 Quiz 2 L02 (Robison, Fall 2014)
October 9
Name:_ (Please, also include your name on the last page as well!)
Student ID:_
This is a closed book exam! Only Scient

Stat 321 Quiz 2 L02 (Robison, Fall 2014) October 9
Name: K51 (Please, also include your name on the last page as well!)
Student ID: ME"
This is a closed book exam! Only Scientific calculators are permitted [no prog/ graph)
Show all relevant work [formulae

l:'_ " UNIVERSITY OF
JCALGARY
UNIVERSITY OF CALGARY
FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS AND STATISTICS
MIDTERM EXAMINATION
Stat, 321 (Robison) - Fall, 2014
DATE: 23/0ctober/2014 Time: 50 Minutes
Student ID Number:
EXAMINATION RULES
T otal Actual

UNIVERSITY OF CALGARY
FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS AND STATISTICS
MIDTERM EXAMINATION
Stat, 321 (Robison) Fall, 2014
DATE: 23/October/2014
Time: 50 Minutes
Student ID Number:
Last Name:
First Name

!1
Extra Practice questions for quiz 2
1. Suppose the values below represent the grade point averages, corresponding gender
and satisfaction with their program (scale of 1 to 5 with 1 representing unsatisfied and
5 representing very satisfied) of 26 rando

Stat 321 Practice Quiz 1 L02 (Robison, Fall 2015)
Due Sunday Sept 27 11:59pm
Please submit your answers via TopHat for bonus marks. Understand these questions may/may not
be similar to that of the actual quiz on October 1. Ple

Solutions to an example from the bonus assignment
Example
A late-night stargazer sees an object, that is unidentifiable, crash. This person is sure the object
landed in one of three areas; namely: area 50, area 51, or area 52.
Unfortunately, the person is

Some Key Formulas for the Midterm
Law of complement: P(A c ) = 1 P(A)
addition law: P(A B) = P(A) + P(B) P(A B)
Total Law of probability: P(A) =
n
n
P(A | B )P(B ) = P(A B )
i
i=1
i
i
i=1
Total Law of probability simplified: P(A) = P(A B) + P(A B c )
Dem

Some Key Formulas for Quiz 2
Law of complement: P(A c ) = 1 P(A)
addition law: P(A B) = P(A) + P(B) P(A B)
Total Law of probability: P(A) =
n
n
P(A | B )P(B ) = P(A B )
i
i
i
i=1
i=1
Total Law of probability simplified: P(A) = P(A B) + P(A B c )
Demorgan

Statistics 321 (L01): Independent Events; Conditional Probability (May 22)
Independent Events
Definition: Two events, A and B are said to be independent events if and only if the occurrence of one
event (A) does not effect the occurrence of event B. If tw

Statistics 321 (Spring 2015) : Practice Problems Covering Set Operations and
Introduction to Probability
Please attempt the following questions 1, 2, and 3 in the lab of May 14th. The answers are found on the last
page of the lab worksheet. If you have qu

Statistics 321 (Spring 2015) : Linear Functions of Random Variables
Result: Let X1 , X2 , , Xn represent random variables where E(Xi ) = i and V ar(Xi ) = i2 < ,for
i = 1, 2, , n. Additionally, Xi and Xj , for i 6= j, are not necessarily independent rando

Statistics 321 Lab #4: Solutions
Solutions:
1. (a) Defining a random variable X to count how many, out of n = 40, disagree with internet companies
handing over private information to authorities. Each person is treated as a Bernoulli trial (disagree is a

4.6
4.8
a.F(i)=P(Y50= l -P(Y>i)= l -P(l"itrialsarefailures)= l -q.
b. It is easily shown that all three properties hold.
a. The constant k = 6 is required so the density function integrates to l.
b.P(.4s Y5 l)=.648.
c. Same as part b. above.
d. P(Ys .4 |

5.79 Referring to Ex. 5.16, integrating the joint density over the two regions of integration:
0 l+y1 l l-yi
E(Y.Y2)=I Iylyzdyzdyi Iylyzdyzdyl =0
-I 0 0 0
5.80 From Ex. 5.36, fl(y,)= yl +% , 05y] S 1, and f2(yz)= y2 +%, 05y2 S 1. Thus,
E(Y1)= 7/12 and E(Y