Math 425 / Stats 425
Homework 3
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made the calculation.
Printing this file is not required.
1
Math 425 / Stats 425
Homework 4
You must show all work when answering the questions. If the answer to the question is a calculation, be sure to write
down the formula you used or describe how you made the calculation. Printing this file is not required.
1
Math 425 / Stats 425
Homework 1
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made the calculation.
Printing this file is not required.
1
Math 425 / Stats 425
Homework 2
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made the calculation.
Printing this file is not required.
1
Math 425 / Stats 425
Homework 7
You must show all work when answering the questions. If the answer to the question is a calculation, be sure to write
down the formula you used or describe how you made the calculation. Printing this file is not required.
1
PROBLEM # 1:Multiple Choice Choose the correct answer. Each multiple choice question is
worth (4) points.
1.1 _B_ Let X be a discrete random variable with pmf, fX, and cdf, FX. x is given as
1 2 3 4
-1/8 1/8 3/8 3/8
Then Fx (2) is
(A) 1/8 (B) 2/8 (C) 3/8
Homework 4 Solutions
Statistics 426
February 2, 2017
1. (4.12) Let Y = X . Then the pdf of Y , fY (y), is symmetric about 0, giving us
Z
Z
Z
E[Y ] =
yfY (y)dy =
yfY (y)dy
yfY (y)d = 0
0
0
E[X ] = E[X] = 0
E[X] =
2. (4.13)
Z
Z
Z
P (X x)dx =
Z Z t
fX (
X follows an exponential distribution with parameter (or X Exp() if
ex x 0
f (x; ) =
0
otherwise
X follows a Gamma distribution with shape parameter and scale parameter (or X (, ) if
(
1 ex
x0
() x
f (x) =
0
otherwise
where the parameters > 0 and > 0.
Th
Homework 1 Solutions
Statistics 426
January 18, 2017
1. (1.8)Let event B1 = A1 , B2 = A2 \A1 , B3 = A3 \A1 A2 ,., Bn = An \A1 . . . An1 . So
now event B1 , B2 , ., Bn .are mutually disjoint. Applying axiom 3 we get
P (ni=1 Ai )
=
P (ni=1 Bi )
=
n
X
P (Bi
Brief Introduction
Examples:
batteries dont last equally long
This is a course about theoretical statistics. First, what is statistics?
One definition could be: The science which deals with
collection
modeling
analysis
interpretation
over-weight increases
HOMEWORK #0, STATS 426, due Wednesday, Jan. 11
BIOGRAPHY
Your Name:
1. What is your major?
2. What do you foresee to be the most challenge issues for you to resolve
in order to succeed in this class? field.
3. What do you foresee the ways you could use th
Continuous Variables
Stats 426 - Continuous random variables and
probability distributions
Chap. 2
X is continuous if its set of possible values contains an entire interval of
numbers.
The distribution of X is characterized by a probability density functi
STATS 426: Introduction to Theoretical Statistics
Winter 2017
Dr. Naisyin Wang
445E West Hall, e-mail: [email protected]
Lectures: MW 2:30pm-4pm, CHEM 1200.
Course Outline
An introduction to theoretical statistics for students with a background in probab
Counting
Stats 426 - Counting, Permutation, Combination &
Discrete Distribution
Chap. 2
A good number of discrete probability models can be worked out based on
counting formulas.
We consider, undet the product rule,
sampling with replacement (swr)
samplin
HOMEWORK #3, STATS 426, due Wednesday, Feb. 1,
Please make sure that you write down intermediate steps to reach the final
answer.
1. 2.59
2. 2.60
3. 2.62
4. 3.6
5. 3.9
In addition, are X and Y independent of each other? Please justify
your answer.
6. 3.15
HOMEWORK #2, STATS 426, due Wednesday, Jan. 25
Please make sure that you write down intermediate steps to reach the final
answer.
1. 2.21
2. 2.24
3. 2.38
4. 2.48
5. 2.49
6. 2.56
7. Read Proposition D on page 63 and use it to solve 2.66
8. 2.67
Stats 426 - Joint Distributions
Chap. 3
In many experiments there are two or more variables of interest.
Examples:
In an agricultural experiment we might measure: yield, rainfall,
temperature,. . .
In a medical study, we measure a patients height, weight,
Stats 250 Exam 3
Chapter 9- Learning about the Difference in Population Means
Part 1: Distribution for a Difference in Sample Means
Independent Samples can be generated in different ways:
1. Random samples are taken separately from two populations and the
1. Freshman 15: A study was conducted to explore the urban myth that college freshman inevitably gain about
15 pounds by the end of their freshman yearreferred to as the so-called Freshman 15.
A random sample of 66 incoming freshman were recruited for the
Definition
Conditions
p
Population proportion
p1-p2
Difference in population
proportion
Population mean
one-sample
test
d
independent
samples test
# of
Variables
1
2
1
1
1
Population mean difference
1. Random Sample
2. Differences must be normal/CLT
1
2
D
Parameters
p
p1-p2
one-sample
test
d
paired
differences
1-2
independent
samples test
Definition
Null
Hypothesis:
Conditions:
# of
Groups
# of
Variables
Population
proportion
H0: p = _
1. Random sample
2. np>10, n(1-p)>10
For HT: np0 > 10, n(1- p0) > 10
Parameters
Definition
p
Population
proportion
p1-p2
Difference
between two
population
proportion
Null Hypothesis:
H0: p = _
one-sample test
d
paired
differences
Population mean
1-2
independent
samples test
Difference
between two
population means
ANOVA
Mor
1
Digital Actuarial Resources
Equation Study List
(Sample Only Purchase the Full Version)
Society of Actuaries
Exam P: Probability
Introduction:
This compilation of equations is designed to aid the student in preparing for Exam P
(Probability) offered thr
Exam Cheat Sheet
Binomial Coefficient: For r n,
n
m
=
n!
m!(n m)!
represents the number of possible combinations of n objects taken m at a time.
Multinomial Coefficient: For n1 + n2 + + nr = n,
n!
n
=
n1 , n2 , ., nr
n1 !n2 ! nr !
represents the number of
www.coachingactuaries.com
www.facebook.com/coachingactuaries
blog.coachingactuaries.com
P Formula Sheet
1
Copyright 2014 Coaching Actuaries. All Rights Reserved.
www.coachingactuaries.com
2
Copyright 2014 Coaching Actuaries. All Right
Exam I: Information and Practice Problems
Stats 510 Fall 2016
October 5, 2016
Information: The first Midterm Exam will be Thursday, October 13 from 6:00-7:30pm
in the classroom TBA. It will cover the material through the lecture notes on Monday/Oct
10. Yo