MTH410Sl3- Test Student name: June 10t , 2013
PART I
For each of the following multiple-choice questions, choose the best response among those
provided. Please circle one.
1. In the notation below, X is the random variable; E and V refer to the expected v
Review of Lecture 1
Statistics-Descriptive and Inferential Statistics
Populations, Parameters, and Samples, Statistic, Variable
Data & Types of Data
Cross-Sectional vs Time Series Data
Interval, Nominal Data, Ordinal
Graphical descriptive techniques for e
Applied Statistics and Probability for Engineers, 6th edition
March 27, 2014
CHAPTER 3
Section 3-1
cfw_0,1,2,.,1000
3-1.
The range of X is
3-2.
The range of X is cfw_0,12
, ,.,50
3-3.
The range of X is cfw_0,12
, ,.,99999
3-4.
The range of X is cfw_0, 1,
Small Sample [n<30]
1 Population
Case 1
ND population
Small Sample (n<30)
is KNOWN!
Use Z distribution
( )
Case 2
ND population
Small Sample (n<30)
is UNKNOWN!
Use t distribution
( )
2 Populations
Case 1
2 ND populations
2 Small Samples
1, 2 are KNOWN!
Large Sample [n>30]
Case 1: ( ) One Sample with a mean
ND population
Large Sample (n>30)
Case 2 : (
( )
Two samples with a two means
ND population
Large Samples (n>30)
(
)
Case 3: ( ) One sample with population proportion
ND population
Large Sample (n>30)
Outline
Confidence interval on the mean, variance known
t distribution
Confidence interval on the mean of a Normal distribution, variance known
2 -distribution
Confidence interval on the variance of a Normal distribution
Practice Problems
March 17, 2016
1
Review of Lecture 2
Probability
Set Theory
Conditional Probability
Independence
Sequential Experiments and Tree Diagrams
Bayes Theorem
MTH410 - S16 - Lecture 03
1/60
Lecture 03
Counting
Random Variables
Mathematical Expectation
Binomial Distribution
MTH41
Outline
Idea of sampling and Random samples
Central Limit Theorem
()
March 8, 2016
1/9
Idea of sampling
In practice, we always regard a population as a random variable X . Lets now explain what
observations mean.
()
March 8, 2016
2/9
Idea of sampling
In p
Outline
Population proportion
Point estimation on a population proportion
Large sample confidence interval for a population proportion
Practice Problems
March 17, 2016
1/9
Population proportion
In many problems we are interested to estimate the proportion
Outline
Continuous Uniform Distribution
Normal Distribution
Standardizing a Normal Distribution
Normal Approximation
Practice Problems
February 12, 2016
1 / 18
Continuous Uniform Distribution
Definition
A continuous random variable X with probability dens
Outline
Review of dicrete random variables: part I
Continuous random variables: probability density function
Continuous random variables: cumulative distribution function
Review of dicrete random variables: part II
Continuous random variables: mean and va
Outline
Point estimation
Special point estimator I: Moments Estimatorss
Special point estimator II: Maximum likelihood estimators
Practice Problems
()
March 8, 2016
1 / 20
Point estimation
Definition
of a
Let be a parameter of a poppulation. A point esti
Outline
Discrete Uniform Distribution
Binomial Distribution
Geometric and Negative Binomial Distribution
Poisson Distribution
Practice Problems
February 4, 2016
1 / 17
Discrete Uniform Distribution
Definition
A random variable X has uniform distribution i
Outline
Review Practice Problems
Introduction to Statistics
Display data
Analyze data
()
March 8, 2016
1 / 18
Review Practice Problems
Problem 1
Suppose X has a continuous uniform distribution over the interval [1.5, 5.5]. Determine
the following
(a) E (X
Outline
Introduction to Random Variables
Probability Mass Function
Cumulative Distribution Function
Mean and Variance of a Discrete Random Variable
Practice Problems
January 31, 2016
1 / 19
Random Variables
We often evaluate the outcomes of a random exper
Hypothesis Testing Small Sample [n<30]
1 Population
Case 1
ND population
is KNOWN!
Step 1: Hypothesis
Step 2: Test Statistic
Step 3: Decision Rule
Case 2
ND population
is UNKNOWN!
Step 1: Hypothesis
Step 2: Test Statistic
Step 3: Decision Rule
2 Populat
RYERSON UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH 410 - Statistics
Solution of the Midterm Exam - Winter 20171
1A
rough marking scheme is also provided.
MTH 410 - Midterm Exam
- Page 1 -
Winter 2017
Problem 1. The cumulative distribution function of a rand
MTH410 - LAB QUIZZES
1. Quizzes (Jan 23-27)
Problem 1.1. A bin of 100 parts contains 8 that are defective. A sample of 10 parts is selected
at random, without replacement. How many samples contains exactly 3 non-defective parts?
Answer. 92
87 samples con
Exercises '11
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Family Name: _
First Name: _
Student ID: _
Please note:
1. Your problem set must be submitted on this form. Please provide your final, polished
solutions in the spaces provided. Remember, it is an art to write a short yet complete
solution: please practic
MTH410, Problem set 4
.
Problem 2 will be marked
in the LAB
FAMILY NAME:
FIRST NAME:
STUDENT ID:
Please note:
1. Your problem set must be submitted on this form. Please provide your final, polished solutions in the spaces provided.
Remember, it is an a
4. A bearing ball manufacturer is under the assumption that they are producing bearing balls of diameter 60 m. Of
course the actual diameters are normally distributed with mean 60 and variance of 16. Recently there are more than
usual number of boxes of t
HW 5 (From 8.2 &8.3)
1. Due to the decrease in interest rates, the First Citizens Bank received a lot
of mortgage applications. A recent sample of 50 mortgage loans resulted
in an average of $257,300. Assume a population standard deviation of
$25,000. If
MTH410- Spring 2016
Lab 5 Examples for BB June 13-17, 2016
1.
2.
Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has
an exponential distribution with = 1, compute the following:
a. The expected time between tw