COUNTING RULE
Counting Rule to Find Total Outcomes
If an experiment consists of three steps and if the first step can
result in m outcomes, the second step in n outcomes, and the
third in k outcomes, then
Total outcomes for the experiment = m n k
Examp
Application: Two-Way ANOVA
Two-way ANOVA enables researchers to study the effects of a variable upon two independent
variables at multiple levels. Researchers might wish to compare the exercise habits (represented
by number of steps taken per month) of in
Hint for problem 8 in Webwork HW 8
Question 8: Let A, B, and C be independent random variables, uniformly distributed
over [0, 10], [0, 7], and [0, 9], respectively. What is the probability that both roots of the
equation Ax2 + Bx + C = 0 are real?
There
[Chapter 6. Functions of
Random Variables]
6.1 Introduction
6.2 Finding the probability distribution of a
function of random variables
6.3 The method of distribution functions
6.5 The method of Moment-generating functions
1
6.1 Introduction
Objective of s
[Chapter 5. Multivariate
Probability Distributions]
5.1 Introduction
5.2 Bivariate and Multivariate probability distributions
5.3 Marginal and Conditional probability distributions
5.4 Independent random variables
5.5 The expected value of a function of r
[Chapter 5. Multivariate
Probability Distributions]
5.1 Introduction
5.2 Bivariate and Multivariate probability distributions
5.3 Marginal and Conditional probability distributions
5.4 Independent random variables
5.5 The expected value of a function of r
Chapter 4. Continuous Random
Variables and Their Probability
Distributions
4.1 Introduction
4.2 The Probability distribution for a continuous random variable
4.3 Expected value for continuous random variables
4.4-4.6 Well-known discrete probability distri
Chapter 3. Discrete Random Variables
and Their Probability Distributions
1
3.4-3 The Binomial random variable
The Binomial random variable is related to binomial experiments
(Def 3.6)
1. The experiment consists of n identical and independent trials.
2. Ea
Chapter 3. Discrete Random Variables
and Their Probability Distributions
1
2.11 Denition of random variable
It frequently occurs that we are mainly interested in some functions of the outcomes as
opposed to the outcome itself. In the example what we do is
2.7 Conditional probability
1
(Def 2.9) The conditional probability of an
event A, given that an event B has occurred
(simply probability of A given B), is equal to
P (A B)
P (A|B) =
P (B)
provided P (B) > 0. P (A|B) is read probability
of A given B.
P (
(Def 2.6) [Denition of probability] Suppose S
is a sample space associated with an experiment. To every event A in S(A is a subset
of S) we assign a number, P (A), called the
probability of A, so that the following axioms
hold:
Axiom 1 : 0 P (A) 1.
Axiom
Exam 2 practice exam solution
Question 1
Question 2
more extreme than yours.
Question 3
Question 4
Question 5
Question 9
I believe the population mean is lower than 69 inches, otherwise it would be difficult to find a sample with average 66.
Question 10
I
Calculating Factorials, Combinations, and Permutations
Factorials
A common function needed to compute probabilities is the
factorial function. The notation for the factorial of n is n! The
! function is found by pressing
menu.
and selecting the PRB
To fin
Chapter 8.4
Estimation of a population proportion large
samples
Recall: The population and sample proportions,
p
denoted by p and ,
respectively, are calculated
X
x
as
p
and p
N
n
where
N=totalnumberofelementsinthepopulation
n=totalnumberofelementsinthes
Chapter 9.1 and 9.2 : Testing hypotheses
about a population mean
Example1 .Suppose that a pharmaceutical
company is concerned whether the mean potency
of an antibiotic meet the minimum government
potency standards. They need to decide between
two possi
Chapter 2.
Organizing and graphing data.
Graphing data is the first and often most
important step in data analysis
The following handout discuss common
graphs for qualitative and quantitative
variables.
1
Example 1
In 1969 the war in Vietnam was at its he
Bivariate Data part 1 (both
variables are categorical)
When two variables are measured on a single
experimental unit, the resulting data are called
bivariate data (height and weight).
You can describe each variable individually,
and you can also explore t
Chapter 6. The Normal Probability
Distribution
A continuous random variable is usually associated with
measurement, and can take on any value in some interval.
(Think of a discrete random variable whose range of values
becomes denser and denser.)
Examples
8.3 ESTIMATION OF A POPULATION MEAN: NOT
KNOWN
Most likely we dont know the true population
standard deviation
x
is not normal!
s/ n
Gossets t
William S. Gosset, an employee of the Guinness
Brewery in Dublin, Ireland, worked long and hard to find
out wh
Chapter 1.
1.1.What is statistics?
The field of statistics is evolving and growing
in ways few imagined even 15 years ago.
The field of statistics has been around for
centuries, yet its significance to society and
the economy is possibly greater today tha
Chapter 3.1 and 3.2
Numerical descriptive measures
Graphs provide a global/qualitative description of
a sample, but they are imprecise for use in
statistical inferences.
We use numerical measures which can be
calculated for either a sample (these measures
CH 7.6 POPULATION AND SAMPLE
PROPORTIONs
Many surveys and experiments are
conducted in order to estimate a population
proportion, the true fraction of individuals or
objects that exhibit a specific characteristic.
For example: pollsters routinely estima
Measures of central tendency (ungrouped data)
Chapter 3.1 and 3.2
Numerical descriptive measures
The mode: is the sample value that occurs most
frequently.
The median: is the value that falls in the middle
position when the sample values are ordered from