STAT2800: Lecture 11
CHAPTER 4: COMMONLY USED DISTRIBUTIONS
The Central Limit Theorem (Section 4.11, page 289)
The Central Limit Theorem is by far the most important result in
statistics. Many commonly used statistical methods rely on this
theorem for the
0
STAT 2800U
MIDTERM: MARCH 9, 2016
First Name
Last Name
Student Number
INSTRUCTIONS:
Use a pen to fill in the front page. All midterm answers
should be written in ink. No white-out is allowed. If a
midterm is written in pencil, you will not be allowed t
STAT2800: Lecture 11
CHAPTER 4: COMMONLY USED DISTRIBUTIONS
The Central Limit Theorem (Section 4.11, page 289)
The Central Limit Theorem is by far the most important result in
statistics. Many commonly used statistical methods rely on this
theorem for the
STAT2800: Lecture 10
CHAPTER 4: COMMONLY USED DISTRIBUTIONS
The Exponential Distribution Contd (Section 4.7, page
262)
Recall: Last class we introduced the Exponential distribution:
Definition
A variable X is said to have an exponential distribution with
STAT2800: Lecture 9
CHAPTER 4: COMMONLY USED DISTRIBUTIONS
The Normal Distribution- Contd (Section 4.5, page 241)
Recall: Last class we focused on applications with the use of the
Normal Distribution. Now lets take a look at the mean and variance
for a No
STAT2800U: Lecture 8
CHAPTER 4: COMMONLY USED DISTRIBUTIONS
The Normal Distribution (Section 4.5, page 241)
Definition
A continuous variable x is said to have a normal distribution with
parameters and , where and 0 , if the
density function of x is
f ( x)
STAT2800U: Lecture 7
CHAPTER 4: COMMONLY USED DISTRIBUTIONS
The Binomial Distribution Contd (Section 4.2, page
203)
THE BINOMIAL DISTRIBUTION (discrete)
Recall: p(x) = proportion of batches with x Ss (successes)
Summary for Binomial Distribution:
If a tot
STAT2800U: Lecture 6
CHAPTER 2: PROBABILITY
Random Variables Contd (Section 2.4, page 88)
Recall: Last class we started setting up discrete random
variables and we also worked with continuous random variables,
lets continue with both:
Example: Two cards a
STAT2800U: Lecture 5
CHAPTER 2: PROBABILITY
Random Variables (Section 2.4, page 88)
Definition:
A numerical characteristic whose value depends on the outcome of a
chance experiment is called a random variable. A random variable
is discrete if its possible
STAT2800U: Lecture 4
CHAPTER 2: PROBABILITY
Counting Methods (Section 2.2, page 62)
Permutations:
In how many ways can you order the letters A, B, C?
Five lifeguards are available for duty one Saturday afternoon. There
are three lifeguard stations. In how
STAT2800U: Lecture 3
CHAPTER 2: PROBABILITY
A chance experiment, also called a random experiment, is simply
an activity or situation whose outcomes, to some degree, depend on
chance. To decide whether a given activity qualifies as a chance
experiment, ask
STAT2800U: Lecture 2
CHAPTER 1: SAMPLING AND DESCRIPTIVE
STATISTICS
Graphical Summaries (Section 1.3, page 25)
Stem-and-Leaf Plots
Most of us already know what a histogram looks like:
Although a histogram tells us how many observations fall in a
particula
STAT2800U: Lecture 1
CHAPTER 1: SAMPLING AND DESCRIPTIVE
STATISTICS
Question: What is a statistic?
Answer: Any numerical summary measure based on data from a
sample; contrasts with a parameter which is based on data from a
population.
Basic Idea of Statis
STAT 2800U
MIDTERM: FEBRUARY 14, 2008
First Name
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INSTRUCTIONS:
Use a pen to fill in the front page. All midterm answers
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1
1. (12 marks) The following scores represent a nurses assessment (X) and a physicians
assessment (Y) of the condition of 10 patients at time of admission to a trauma center.
X: 18
13
18
15
10
12
8
4
7
3
Y: 23
20
18
16
14
11
10
7
6
4
(a)
Compute the samp
SitisziCS..431?"Prmabg. .. QC??? 2003........... .. .. .. . 2
1. (8 marks) If x is & binomiai random variabie with parameters 2% and
Show that the mean of the random variable 1: is {6 marks}
{b} If n 2 10 and 7? z Find P{x m 10) {ii} P{:I
STAT 2800U
MIDTERM: MARCH 1, 2006
First Name
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Signature of Student
INSTRUCTIONS:
Use a pen to fill in the front page. All midterm answers
should be written in ink. No white-out is allowed. If a
midterm is written in pencil, you wi
99
February 9 2009, Lecture 11:
MIDTERM REVIEW
1. Chapter 1 is pretty straight forward. Please make sure you
understand your simple summary statistics of a raw data set
(i.e., x, s 2 , ~ , quartiles, etc). Also, please understand the three
x
graphical sum
§ZFAT28OO Midterm < Wlfvlar 5, 2910 > _ 2
1. (8 marks) If :r is a binomial random variable with parameters n and 7T,
72
(a) Evaluate Z 51:2 7r? (1 ~7r)x [Note: this summation is not the formula
:6
22:0
for the variance of the binomial distribution, bu
Midterm Formula Sheet for STAT 2800
Lognormal Distribution:
Discrete Distribution:
Mean: x = x p( x)
Variance: = ( x ) p ( x)
Continuous Distribution:
Mean: x = x f ( x)dx
2
x
2
where
x
(x ) f (x)dx
2
z=
ln x
+
2
Mean: E (Y ) = e 2
Variance: V (Y ) = e 2
STAT 2800U
MIDTERM: FEBRUARY 15, 2007
First Name
Last Name
Student Number
Signature of Student
TAs Name
INSTRUCTIONS:
Use a pen to fill in the front page. All midterm answers
should be written in ink. No white-out is allowed. If a
midterm is written in p