Weighted Means and Grouped Data (Section 2.8)
(I)
Weighted Means
In calculating the mean of a population or sample, we sum each measurement and divide
by the number of measurements
that is, each measurement is given the same importance or weight
But some
Applied Probability and Statistics
for Engineers
Course SS2141 Contents 2015 Fall Term
R. Zitikis
Department of Statistical and Actuarial Sciences
The University of Western Ontario
London, Ontario, Canada
September 7, 2015
2
Suggestions
Class attendance
STATS 2035 FINAL EXAM PRACTICE QUESTIONS  1
(Chapters 10, 11, 12, 13, 14.2, 16)
1.
A study was done that took a look at the percentage of females in OECD (Organization for European Collaboration
and Development) countries and former communist countries w
Statistics 2035
Practice Final Exam 2 (Questions from Chapter 10, 11, 12, 13, 14.2, 16)
1.
Six chemists in a laboratory were asked to determine the percentage of methyl alcohol in a certain
compound. Each chemist was randomly assigned five pieces of the c
Statistics 2035 Final Exam Formula Sheet
Confidence Intervals
For 1 2:
( x1 x2 ) z
12
2
n1
+
22
For 1 2 (equal population variances):
where sp2 = pooled variance =
(
d
p 1 p 2 ) z/2
Hypothesis Tests
For tests about 1 2:
( x1 x2 ) t
n2
( x1 x 2 ) t
1
1
Statistical Sciences 2035 Section 001  Final Exam Handout 201516
1. The final exam is scheduled for Tuesday, April 26, 2016, from 2:00 pm to 4:30 pm. It is a
2.5hour multiple choice exam. Please arrive by 1:50 am as we will begin seating students
aroun
Midterm Exam #2 Formula Page
Binomial Distribution: p (x ) =
n!
p x (1 p ) n  x , x = 0, 1, 2, ., n.
x!(n  x )!
x = np,
x2 = np (1 p )
Continuous Random Variables/Distributions
Uniform Distribution: f (x) =
1
ba
, a<x<b
x =
a+b
ba
and x =
2
12
Normal:
STATS 1024 NOTES
CHAPTER 1 Planning Distributions with Graphs
INDIVIDUALS AND VARIABLES



Individual: a person or object on which an observation is made, also known as:
Experimental units
Sampling units
Variable: any characteristic of the individual
(Chapter 19) Confidence Intervals
95% of the time, the mean will fall between these values.
4 step process of calculating confidence intervals:
1.
2.
3.
4.
State what parameter do you want to estimate and at what confidence level?
Plan hypotheses; determi
Stats 1024 Final Notes
Chapter 17: Tests of Significance: The Basics
Logic of testing (simple logic) assume that the statement is true. How likely is the test result? If result is
very likely, the statement may be true. If result is unlikely, then stateme
CH.1 Picturing Distributions with Graphs
Individuals and Variables
An individual is a person or object on which an observation is made.
They are sometimes known as experimental units or sampling units.
A variable is any characteristic of the individual.
Solutions to Selected Questions in Chapter 7
Question 7.3
Using the bond valuation formulas (7.1), (7.3), (7.6) we obtain the following yields and
prices:
ZeroCoupon
Bond Yield
ZeroCoupon
Bond Price
OneYear
Implied Forward
Rate
Par
Coupon
Cont. Comp.
Z
Solutions to Problem Set 5
Ex5.2 5.10 (even), ex5.11  5.15(a)(d), and ex5.17
Ex9.1  9.3, ex9.16 and ex9.17.
Question 5.2
a) The owner of the stock is entitled to receive dividends. As we will get the stock only
in one year, the value of the prepaid fo
An additional example for Chapter 7
1. You observe the following six bond prices from the market. All coupons are distributed every
6month for coupon bearing bonds. Using Bootstrap method to derive zerocoupon bond
prices and plot the yield curve based o
Solutions to the Selected Questions in Chapter 8
Ex 8.28.8 (even numbered) and 8.14
Question 8.2
a) We first solve for the present value of the cost per three barrels, based on the forward
prices:
$21
$22
$20
+
+
= 55.3413.
2
(1.07)3
1.06 (1.065)
We then
FM2557 Midterm Test 1
February 2, 2016
First name: _ Last name _
Student Number: _
Instructions:
This is a 60minute closedbook exam.
Only nonprogrammable calculators are permitted.
There are 4 questions and 50 points in total. The number of points
EXAM CODE: 111 March 14, 2005
University of Western Ontario
Department of Statistical and Actuarial Sciences
Statistical Sciences 241b/243b Midterm #2
Name: COQ me ME) if cfw_k
Student Number: W
STEP 1: Fill in your NAME and STUDENT NUMBER above and on th
Practice Questions for Midterm #2
Note: Correct answers for multiple choice questions are in bold print.
Multiple Choice Questions
1. To estimate the mean number of days absent last year among its 600
employees, ABC Manufacturing took a random sample of 2
igitiitsheszfliili Preoifce Midterm Exam
1. Suppose A and B are eyents such that P(A) = 0.20, P(B) = 0.40. Assuming that A and B are mutually exclusive
events, what is the probability that at least one of these two events occurs?
(A) 0.225 (B) 0.080 (C) 0
ch49
sX
+0de 2.14410  7.604 ~ cfw_Dickierm gram
1. Two events, A and B. are independent, both with probability 0.3. What is P (A " U B f)?
(A) 0.91 (B) 0.51 (C) 0.49 (D) 0.09
2. You are given the following cumulative distribution function for a discrete
Solutions to the Statistics 2143b Midterm Exam Practice Questions
1.
Answer: A. If A and B are mutually exclusive, then P(A B) = P(A)
+ P(B) = 0.3 + 0.3 = 0.6.
2.
Answer: D. We want P(A or B occurring, but not both). This means
we want P(A) + P(B) 2*P(A B
Statistics 2143b Midterm Exam Practice Questions
1.
If events A and B are mutually exclusive, and each event occurs with probability 0.3, what is
P(A B)?
A)
0.6
B)
0.09
C)
0
D)
0.51
2.
If events A and B are independent, each occurring with probability equ
Statistics 2143b Suggested Text Exercises
Suggested Exercises
The best way to learn a mathbased course (such as this one) is to do exercises from the
textbook. This is the best way to understand how to set up the solution to a problem and
how to do the m
Statistics 2143B Midterm Exam Formula Page
Probability
Addition Rules
P(A B) = P(A) + P(B) P(AB)
P(A B C) = P(A)+P(B)+P(C)P(AB)P(AC)P(BC)+P(ABC)
Conditional Probability
P(A  B) = P ( A B ) = P( A ) P( B  A )
P( B)
P( B)
/
P(B) = P(A B) + P(A B) = P(A) P
Statistics 2143B Midterm Exam Practice Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
A
D
A
B
C
D
C
D
A
D
B
A
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
A
C
D
B
B
B
D
C
C
C
A
B
B