Information for Final Exam, STAT 270
Last update: August 11th, 12:30pm.
WHEN and WHERE.
The Final Exam will be on Thursday August 13th from 3:30pm to 6:30pm in our regular
classroom on Images Theatre.
PROCEDURES.
Please wait outside the classroom until
5/26/2017
Lecture 6
or through Canvas (click on Redirect Tool) in
the navigation pane
Probability
Access at
http:/www.sfu.ca/lectures
Definition and properties
The discrete uniform distribution
Conditional probability
Independence
Most useful for statisti
STAT 270: Lecture 1
Introduction to Probability and Statistics
Rachel Altman
1 / 13
Agenda
1
Course information
2
What is statistics? What is probability?
3
Some examples
2 / 13
Course Information
I will post all course resources (lecture notes, assignmen
5/19/2017
More on descriptive statistics
Percentiles and quartiles
Boxplots
Scatterplots
Correlation
Lecture 4
Other measures of location
and spread
Let p be a number between 0 and 1
The 100pth percentile is the point c such that
at least 100p % of data a
6/30/2017
Lecture 15
Distribution functions for
describing multiple rvs
E.g., our class of 155 students has 55 CS
students, 19 Econ students, and 81 others
Say I choose 10 students, with replacement,
to present solutions to 10 questions
Let
,
,
be t
6/9/2017
On Wed., June 14
I will be away
Jack Davis will lead a problem-solving session (Ch.
4 material)
No office hours
Lecture 10
On Thurs., June 15
I will have office hours 2-3pm
Midterm
pmfs
Cumulative distribution functions (cdfs)
Expected value
6/2/2017
Counting rules
Product rule
Permutation rule
Combination rule
Lecture 8
Products, permutations, and
combinations
Let an experiment, E, be comprised of k
smaller experiments, E1, E2,Ek.
The number of outcomes in E is
#E=(#E1)(#E2)(#Ek)
E.g., fl
STAT 270: Lecture 2
Introduction to Probability and Statistics
Rachel Altman
1 / 11
Agenda
1
Summary statistics
2
Some statistical language
2 / 11
Question: Do Girls Text More than Boys, on Average?
Is texting taking a toll on you1 ?
Overall, girls text c
7/7/2017
Statistics (definition, examples)
Central limit theorem
Lecture 17
Definition and examples
A random sample is a collection of rvs,
, , , that are independent and identically
distributed (iid)
(Confusingly) a random sample could also
refer to rea
Problem (FROM Lecture 11): A library subscribes to two weekly magazines, each of which is suppose to
arrive on Wednesdays. In actuality, the two magazines arrive independently with probabilities of arrival,
P(Wed) = 0.3, P(Thu) = 0.4, P(Fri) = 0.2 and P(S
Problem: (Lecture 14, page1) A friend recently planned a camping trip. He had two
flashlights, one that required a single 6-V battery and another that used two size-D batteries. He
had previously packed two 6-V and four size-D batteries in his camper. Sup
Lecture 20
Problem: The weight distribution of parcels is normal with mean value 12lb and std dev 3.5lb.
The parcel service wants to establish a weight c beyond which there is a surcharge. What is the
value of c such that 99% of parcels are at least 1lb u
Information for Midterm Exam 4, STAT 270
Last update: July 29th, 11:30am.
WHEN and WHERE.
The fourth midterm exam will be on Friday July 31st from 9:30am to 10:20am in our regular
classroom on Images Theatre.
PROCEDURES.
Please wait outside the classroo
1.
Consider X~binomial(1,1/3) independent of Y~binomial(2,1/2). Obtain the pmf of W = XY + 1.
X g 0 CU} f «*v M( \l 3/
\ w 13$ «7w Saab} \1 593 V13 keﬂkw
0
f0rw>0
2. Let the pdf for random variable W be f(w) = f (w) ={ > '
otherwzse.
E( W) Va» C W)
F ind
l. A multiple choice exam has 50 questions. Each question has potential answers A, B, C, D, and
E. The instructor wants to give one mark for a correct answer, zero marks for a non-response
and x marks for an incorrect answer such that someone who guesses
1; 4%
1. (Based on a problem from “Stats, data and models” by De Veaux et a1.) Does how long children
remain at the lunch table help predict how much they eat? The table gives data on 20 toddlers
observed over several months at a nursery school. “Time” i
Information for Midterm Exam 3, STAT 270
Last update: June 8th, 5:00pm.
WHEN and WHERE.
The second midterm exam will be on Friday July 10 th from 9:30am to 10:20am in our regular
classroom on Images Theatre.
PROCEDURES.
Please wait outside the classroom
A coin is ﬂipped until a head appears. What is the probability that a head appears on an odd—
numbered ﬂip? Simplify as much as possible and ShOW work (explaining where needed).
Owiwwes a} "mitt/Psi “14‘ H} Ti” \t) "TTTTllj i}
?V0\00\5\¥E§ Lineag “Q Q‘C’c
Information for Midterm Exam 2, STAT 270
Last update: June 17th, 4:30pm.
WHEN and WHERE.
The second midterm exam will be on Friday June 19th from 9:30am to 10:20am in our regular
classroom on Images Theatre.
PROCEDURES.
Please wait outside the classroom
Information for Midterm Exam 1 STAT 270
Last update: May 28th, 10:00am.
WHEN and WHERE.
The first midterm exam will be on Friday May 29th from 9:30am to 10:20am in our regular
classroom on Images Theatre.
PROCEDURES.
Please wait outside the classroom un
5/18/2017
More on descriptive statistics
Skewness and symmetry
Measures of location
Measures of dispersion
Lecture 3
Describing the shape of a
histogram
Histogram
seems roughly
symmetrical
but beware of
the unequal
bin widths!
Histograms are often desc
Combinatorics Problems
1. How many 4 letter words exist (using the Roman alphabet)?
a. 4!
b. 26!
26
c.
4
d. 264
2. How many ways can a president and vice-president be elected from a group of 10 students?
10
a.
2
b. 102
c. 10!
d. 10(2)
3. How many permut
Suppose have 1000 people in a population (500 male and 500
female) and average age of the males is 26 and average age of
females is 24
What is the mean age in the population?
25 years old
Suppose have 1000 people in a population (900 male and 100
female)
A coin is tossed 2 times
S= cfw_ (H,T), (T,H), (H,H), (T,T)
What is the probability of getting not getting a tails?
Two solutions:
1.
A= (H,H) P(A) =
2.
A^C = (H,H), (T,H), (T,T)
P(A) = 1-P(A^C) = 1-3/4 = 1/4
Example: All outcomes of rolling 2 dice:
(1
Recall that probabilities must lie between 0 and 1
Represent the long term proportion of ties an outcome is observed
based on repeated samples
Use P( ) as shorthand for The probability of ( ),where inside the ( )
you name some event.
Roll a die. What is
NCAA Division II requires that athletes get a combined score of at
least 820 on the SAT exam in order to compete in their first year of
college sports. SAT scores for college-bound students are normally
distributed with a mean of 1012 and standard deviat
Suppose that r2=.81. What does this mean?
Implies that 81% of the observed variation in the GPA scores is
explained by the linear relationship with IQ
What is the correlation?
Correlation is r=0.90 How do we know it is not -0.90?
Must have same sign as t
Earlier, we concerned ourselves with numerical/graphical summaries
of samples (x1, x2, , xn) from some population
Can view each of the Xis as random variables
We will be concerned with random samples
The Xis are independent
The Xis come from the same pop
Observations
Sharper curve = smaller standard deviation
Bigger curve = larger standard deviation
Suppose have a sample of size n from a
distribution
A level C confidence interval is:
[ xBar-Z (sigma/ sqrt n), xBar+Z (sigma/ sqrt n) ]
Xbar = number calcul
Examples of parameters:
Population mean ( eg. Average age of people in the population)
Population proportion (eg. Proportion of people who support
tuition increases)
Examples of statistics:
Sample mean
Sample proportion
A 95% confidence interval is an in
6/23/2017
Continuous random variables
Lecture 13
Cumulative distribution function (cdf)
Example using the exponential cdf
Probability density function (pdf)
Examples (exponential, uniform, normal, gamma)
=
Definition and cdf
Continuous rvs take values in
5/31/2017
Please download from Google Play or the App
Store in time for Fridays class
See my email for instructions
Lecture 7
Independence of events
Counting rules
Product rule
Permutation rule
Combination rule
Relationship between
probabilities of two
6/21/2017
Variance and standard deviation
Poisson process
In Chapter 2 we learned the definition of
Lecture 12
sample variance
Measures of spread of a rv
On a histogram, the sample variance
describes the spread of the observations (a
finite number of real
Combinatorics Problems
1. How many 4 letter words exist (using the Roman alphabet)?
a. 4!
b. 26!
26
c.
4
d. 264
2. How many ways can a president and vice-president be elected from a group of 10 students?
10
a.
2
b. 102
c. 10!
d. 10(2)
3. How many permut
6/8/2017
Discrete random variables
Probability mass function (pmf)
Examples of discrete distributions
Lecture 9
Definition and examples
A random variable (rv) is a real-valued
function of the sample space
E.g., in a family, the possible sexes of 2
childre