11
BINOMIAL DISTRIBUTION
Examples:
1. Five terminals on an on-line computer system are attached to a communication line to the central computer
system. The probability that any terminal is ready to
transmit is 0.95.
Let X denote the number of ready termin
Journal of Economic Cooperation and Development, 34, 3 (2013), 61-100
The Role of Political Stability on Economic Performance:
The Case of Bangladesh
Moin Uddin Ahmed 1 and Mohammad Habibullah Pulok 2
Political stability generally plays pivotal role in th
NATIONAL UNIVERSITY
Syllabus
Department of Statistics
Four Year B.Sc Honours Course
Effective from the
Session : 20092010
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National Univ
Types of data: Statistics
Students need know that data that they collect can be one of several types. It is important to know
what type it is because it helps decide how best to collect it and appropriate ways to display it.
The first distinction is betwe
1
Sufficient Statistics
When the population is modeled by a probability distribution or probability
density function that depends on a parameter , we collect a random sample
to make inferences about . For any particular family of distributions f (x|),
is
VARIABLES
Topic #3
Variables and the Unit of Analysis
Variables are characteristics of the things that we are
studying.
These things are commonly called cases or units.
A case study focuses on a single thing.
The kind of thing that is being studied is
Module 2: Types of Data
This module describes the types of data typically
encountered in public health applications.
Recognizing and understanding the different data
types is an important component of proper data use
and interpretation.
Reviewed 15 April
Types of Variables
AP Statistics
06-07
Dobson
Review of Terms
Individual: The objects described by a
set of data, individuals may be people,
animals or things
Ex: Students in an AP Statistics class
Variable: any characteristic of an
individual. A variable
Presentation 2
Summarizing One or Two Categorical Variables
&
Relationships Between Categorical Variables
Types of Variables
Categorical Possible values define group or categories,
not necessarily in an apparent ordering
Ex. Color of M&Ms
Gender
Stat 200
ANOVA in R
1-Way ANOVA
Were going to use a data set called InsectSprays. 6 different insect sprays (1 Independent
Variable with 6 levels) were tested to see if there was a difference in the number of insects
found in the field after each spraying (Depende
Class Practice on Hypothesis Testing #4 Homework Problems
1. The college bookstore tells prospective students that the average cost of its
textbooks is $52 with a standard deviation of $4.50. A group of smart statistics
students thinks that the average co
www.ck12.org
Chapter 12. Hypothesis Testing
C HAPTER
12
Hypothesis Testing
Chapter Outline
12.1
H YPOTHESIS T ESTING
12.2
C RITICAL VALUES
12.3
O NE -S AMPLE T T EST
247
12.1. Hypothesis Testing
www.ck12.org
12.1 Hypothesis Testing
Learning Objectives
De
Hypothesis Testing Examples
1.
Suppose we would like to determine if the typical amount spent per customer
for dinner at a new restaurant in town is more than $20.00. A sample of 49
customers over a three-week period was randomly selected and the average
Introduction to statistics and data
Types of Variables: Overview
Categorical
Quantitative
Descriptive Statistics
Categorical Variables
Dichotomous (binary) two levels
binary
nominal
ordinal
discrete
continuous
2 categories +
more categories +
order matter
Chapter 4
Linear Estimation Theory
Virtually all branches of science, engineering, and social science for data analysis, system control subject to random disturbances or for decision making based on incomplete
information call for estimation theory.
Man
Chapter 2
Fundamentals of Statistics
This chapter discusses some fundamental concepts of mathematical statistics. These concepts are essential for the material in later chapters.
2.1 Populations, Samples, and Models
A typical statistical problem can be de
R Lab Session : Part 2
To see a review of how to start R, look at the beginning of Lab1 http:/www-stat.stanford.edu/ epurdom/RLab.htm
Probability Calculations
The following examples demonstrate how to calculate the value of the cumulative distribution
fun
Hypergeometric Distribution
Suppose an urn contains w white balls and b black balls
for a total of T = w + b balls (the population size)
and that a sample of size n is drawn without replacement.
Let X = # of white balls in the sample of n.
We seek the dis
12
HYPERGEOMETRIC DISTRIBUTION
Examples:
1. Five cards are chosen from a well shuffled deck.
X = the number of diamonds selected.
2. An audio amplifier contains six transistors. It has been
ascertained that three of the transistors are faulty but
it is no
Page R10.1
R TUTORIAL, #10:
BINOMIAL DISTRIBUTIONS
The (>) symbol indicates something that you will type in.
A bullet () indicates what the R program should output (and other comments).
BINOMIAL COEFFICIENTS, PASCALS TRIANGLE, and LOOPS
5
Find , or 5 C2
13
POISSON DISTRIBUTION
Examples
1. You have observed that the number of hits to your web
site occur at a rate of 2 a day.
Let X be be the number of hits in a day
2. You observe that the number of telephone calls that
arrive each day on your mobile phone
Will Murrays Probability, XIV. Negative Binomial Distribution 1
XIV. Negative Binomial Distribution
Negative Binomial Distribution
The
negative
binomial
distribution
describes a sequence of trials, each of
which can have two outcomes (success or
failure).
King Abdul Aziz University
Department of Statistics
Assignment 6
Stat 271
Term 1, 2013
Name:_
ID:_
Section:_
Marks Obtained:_
Please attach the output using megastat along with the assignment
The due date next Saturday & Sunday 24 and 25/1/1434
y
1. The f
Hyper Geometric
1. A sample of 3 items is selected at random from a box containing 20 items of
which 4 are defective. Find the expected number of defective items in the
sample.
2. Suppose that a batch of 100 items contains 6 that are defective and 94 that
Counting
1. (a) How many different 7-place license plates are possible if the first 2 places are for
letters and the other 5 for numbers?
(b) Repeat part (a) under the assumption that no letter or number can be repeated in a
single license plate.
2. How m
Stem-and-Leaf Display
A stem-and-leaf display resembles a histogram which is useful for
quantitative data sets. The purpose of a stem-and-leaf display is
similar to a histogram.
A stem-and-leaf display provides the following information:
(i) range of the
Joint Probability Distributions
1. Suppose that 2 balls are randomly selected from a box containing 3 red, 4 white, and
5 blue balls. If we let X and Y denote, respectively, the number of red and white balls
chosen. Construct the joint probability mass fu
Lecture 5: Estimation
Goals
Basic concepts of estimation
Statistical approaches for estimating parameters
Parametric interval estimation
Nonparametric interval estimation (bootstrap)
Central Dogma of Statistics
Probability
Population
Descriptive
Stati
4.44.5 Geometric and Negative Binomial
Distributions
Prof. Tesler
Math 186
February 5, 2014
Prof. Tesler
4.4-4.5 Geometric & Negative Binomial DistributionsMath 186 / February 5, 2014
1/8
Geometric Distribution
Consider a biased coin with probability p of
One-way ANOVA
We are often interested in determining whether the means from more than two
populations or groups are equal or not. To test whether the difference in means
is statistically significant we can perform analysis of variance (ANOVA) using the
R