Probability & Statistics -- MA 120, PUCIT

Probability & Statistics (MA 120)
Fall 2020

Lectures:

Monday and Wednesday 11:30 am - 01:00 pm Google Meet

Office Hours:

Monday 02:00 pm - 03:00 pm Google Meet

Online Grading Scheme/Criteria:

Quizzes 35%

Mid-Term 15%

Final 50%

Texts:
Lectures on Probability Theory, Khan and Khan, Manuscript in preparation
Statistics - A First Course, Freund, John and Perles, Benjamin, 8th Edition, Pearson Prentice Hall, Upper Saddle River, New Jersey, 2004.
Statistics, Freedman, Pisani, and Purves, 4th edition, W.W. Norton and Co., New York, 2007.

Interesting Links:

Why Do People Find Probability Unintuitive and Difficult?

Grades:
Grading sheet (Accessible only through your PUCIT email account)

Content

#	Topic	Video	Reading	Practice Sets
1	Introduction In order to understand the "real" world Statistics are important for summarizing data Probability is the tool	[Video]	Lecture 1
2	How to Compute Probability? Empirical vs Counting Approach Empirical Approach Counting Approach Axioms of Probability	[Video]
3	Some Rules and Proofs in Probability	[Video]		Practice Set 1
4	Types of Sample Spaces Finite Countably Infinite Uncountable Infinite Simple Sample Space	[Video]	Lecture 2
5	Multiplication Principle and Permutations Multiplication Principle Permutation (ordered arangement of distinct objects)	[Video]
6	Combinations Combination (unordered arangement of distinct objects) C(n,k)=P(n,k)/k!	[Video]		Practice Set 2
7	Hypergeometric and Multinomial Counting Hypergeometric counting Multinomial Combinations (unordered arrangement of multiple types of distinct objects) Probability for Countably Infinite Sample Spaces Computing probability in a countably infinite sample space	[Video A] [Video B]		Discussion of Practice Sets 1 and 2 Further Discussion
8	Probability via Measurement Length Area Volume Non-equilikely spaces	[Video]	Lecture 3	Practice Set 3
9	Independence Independent events Mutually exlusive events	[Video]	Lecture 4
10	Bernoulli and Binomial Experiments Bernoulli experiment Bernoulli process Binomial experiment	[Video]		Practice Set 4
11	Random Variables Mapping between singleton events and real numbers Partition of S Probability Density Function Discrete vs Continous RVs Cumulative Distribution Function	[Video]	Lecture 5
12	Discrete Random Variables Binomial Poisson Geometric Shifted Geometric Negative Binomial Shifted Negative Binomial	[Video A] [Video B]	Lecture 6
13	Continuous Random Variables - I Density function is not equal to the probability function Non-negative function with area 1 is a density function Empirical distribution --> Histogram --> Approximating density function	[Video]	Lecture 7	Discussion of Practice Set 4
14	Continuous Random Variables - II Uniform Density Normal Density Standard Normal Density The 68-95-99 Rule	[Video]	Lecture 8	Practice Set 5
15	Normal Approximation Standard Normal Table Normal Approximation to Binomial Density Dedicated to the memory of Uneeb Nasir (Fall'11).	[Video]
16	Expectation Expectation of a Random Variable Properties of Expectation Expectation of Binomial Random Variable	[Video]	Lecture 9
17	Variance Moments of a Random Variable Variance of a Random Variable Properties of Variance	[Video]
18	Conditional Probability Conditional Event Restriction of Sample Space P(A\|B)=P(AB)/P(B) Properties of Conditional Probability Theorem of Total Probability Bayes' Theorem	[Video]		Practice Set 6
19	Central Limit Theorem I.I.D Random Variables Central Limit Theorem Box Models	[Video]		Practice Set 7
20	Introduction to Statistics Some Terminology N-value Census vs Survey Population vs Sample Parameter vs Statistic Capture-Recapture method for determining N-value Sampling Methods	[Video]
21	Sampling and Studies Sampling Methods Convenience Quota Simple Random Stratified Correlation is not causation Studies Observational Double-blind, randomized, placebo-controlled	[Video A] [Video B]
22	Descriptive Statistics Visual Bar Chart Line Graph Pictogram Pie Chart Histogram Numerical Measures of Location Mean Median Quartiles Percentiles Box-Whisker Plot Measures of Spread Range Inter-quartile Range Standard Deviation	[Video A] [Video B]
23	Correlation Bivariate Data Strength of association How does correlation measure strength of association? Correlation is only for linear association Outliers affect correlation	[Video]