STAT401 PSE Part 1

Nao Mimoto, Dept of Statistics, U of Akron Back to Class Webpage

1A - What is Statistics?

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1B - Descriptive Statistics

Univariate, bivariate, and multivariate data
Ex: Speed of Light Data
Population vs Sample
Histogram, and Frequency vs Relative Frequency
Sample Mean, Sample Variance and Sample SD
Five Number Summary
Get quartiles by INCLUDING the median
Inter-Quartile Range is (Q3 - Q1):
Use 5 number summary to draw a box-plot
Outlier
Relate Histogram and Boxplot
Be able to calculate variance by hand
Mean is larger than Median for right skewed data
Mean is much more sensitive than Median
Can you get quantiles by looking at Histogram

2A - Probability Basics

Probability and Statistics
What does Prob = 1/6 mean?
It means Rel Freq converges to 1/6 if $n$ is large
Statistics and Probability
We see prob only when $n$ is 'large'
Sample Space and Events
Ex: Roll a die
When each outcome is equally likely
Ex: Flip a coin twice
Ex: Kids Next Door
Ex: Sum of two dice
What if $X=$minimum of two numbers

2B - Counting Techniques

Counting Formulas
Orderd, without Replacement (Permutations)
Unordered, without Replacement (Combination)
Binomial Coefficient
Ex: Batting Orders
Ex: 20 people in a party
Ex: Binomial Expansion
Ex: Kids and Gifts

2C - Probability through Counting

Ex: Batting Orders
Ex: Boys and Girls
Ex: Fake or Real
Ex: Three Kind in a Box

2D - Probability Through Set Operation

Set Operations
Distributive law of unions and intersections
DeMorgan's law
Axioms of probability
Probability Formulas
Ex: Project Funding
Ex: Lab (work vs Referral)
Inc-Exc Extended

2E + F - Cond. Prob. and Independence

Conditional Probability
Ex: Defective/Non-defective
Independence
Complements are also independent
How the table look under independence
Ex: Aircraft Seam
Ex: Free-Throws

3A - Discrete Random Variable

PMF and CDF
Ex: Roll a Die Once
Ex: Roll a Die Twice
Ex: get CDF from pmf
Ex: get pmf from CDF

3B - Expectation (Theoretical Mean)

Ex: Throw a Die Once
Expectation is a long-run average
Ex: Pooled Blood Testing
Ex: Casino Simplified
How to calculate E(g(X))

3C - Variance (Theoretical)

Alternative formula for variance
Ex: Throw a Die Once

3D - Binomial(n,p) Distribution

Binomial(n,p) on TI-84
Derivation of Binomial pmf
Ex: Multiple Choice Exam
Ex: Free-throw

3E - Poisson Distribution

Poisson as a limit of Binomial
When Time Units are Changed
Ex: Number of Tornados
Ex: Aircraft arrivals

Part 1 goes to Midterm 1

This covers all material upto Midterm 1. Take Quiz 1, 2, 3 before attempting the M1.

STAT401 PSE

Part 1
week1 through week4

Part 2
week5 through week8

Part 3
week9 through week12

Part 4
week13 through week15