Probability & Statistics (MA 120)
Fall 2019

Dr. Nazar Khan

Lectures:

	Morning (Room 3)	Afternoon (Room 3)
Monday and Wednesday	11:30 am - 01:00 pm	02:30 pm - 04:00 pm

Office Hours:

Monday

04:30 pm - 05:30 pm

Grading Scheme/Criteria:

Quizes	20%
Assignments	5%
Mid-Term	35%
Final	40%

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

Interesting Links:

Why Do People Find Probability Unintuitive and Difficult?

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

Content

1. Introduction
   • In order to understand the "real" world
   • Statistics are important for summarizing data
   • Probability is the tool
2. Statistics
   • Design of Experiments
   • Descriptive Statistics
   • Stem-and-leaf Display
   • Frequency Distribution
   • Histogram
   • Bar Chart, Pictogram, Pie Chart
   • Mean and Weighted-Mean
   • Median
   • Robustness in the presence of outliers
   • Computation via stem-and-leaf display
   • Quartiles and Percentiles
   • Box-and-whisker plot
   • Mode
   • Standard Deviation
   • Interpreting Histograms
3. Probability
   • Counting
   • Multiplication Principle.
   • Permutations (when order matters).
   • Combinations (when order does not matter).
   • Introduction to Probability
     • Predictions in the presence of uncertainty.
     • Expectation
     • Random Experiment, Outcome.
     • Sample Space (S), Events (E), Probabilities of Events (P).
     • Probability Space (S,E,P)
     • Set Theory and Venn Diagrams
     • Mutual Exclusion
     • Axioms of Probability
   • Methods for Computing Probability
     • Counting Elements (when S is a simple sample space).
     • Measuring Sizes (when S is not a simple sample space).
   • Independence
   • Joint Probability
   • Multiplication rule for statistical independence
   • Conditional Probability
   • Restricted sample space
   • Theorem of Total Probability (TTP)
   • Bayes' rule
   • Random Variables and Probability Distributions
   • Discrete
   • Binomial
   • Geometric
   • Shifted Geometric
   • Negative Binomial
   • Shifted Negative Binomial
   • Multinomial
   • Hypergeometric
   • Poisson
   • Continuous
   • Probability Density vs. Probability Mass
   • Normal Density -- Queen of densities
   • Standard Normal Density
   • Standardization
   • z-score = amount of standard deviations away from the mean
   • Standard Normal Table
   • Normal approximation to discrete densities
   • Continuity correction
   • Normal approximation of Binomial density
4. Expectations
5. Multivariate Distributions
6. Conditional Probability
7. Law of Large Numbers and the Central Limit Theorem
8. Box Models
9. Tests of Significance
10. Applications
    • Model Fitting
    • Pattern Classification