& Computational Probability
Text & Syllabus
Textbook: Instructor's Notes and SOCR resource pages
three hours; discussion, one hour. Requisites: Mathematics 31A, Program
in Computing 10A.
Basic introductory probability topics in interactive
problem-driven manner. Various applets, interfaces, and demonstrations
used to illustrate fundamental properties of distributions, random
number generation, combinatorics, expectation, variability, and
sampling. Assignment of projects that require light computer
programming. Emphasis on practical description, utilization, and
graphical presentation of various probabilistic modeling techniques.
P/NP or letter grading.
Tentative schedule of topics to be
- Probability, data analysis, sampling theory and statistical inference.
- Basic Probability
- Probability models, sample space, events, “some” algebra of
- Probability axioms, combinatorial problems, conditional
probability, independent events, Bayes’ rule, Bernoulli trials.
random variables, probability mass function, cumulative distribution
special discrete distributions (Bernoulli, Binomial, geometric,
binomial, poisson, hypergeometric, discrete uniform), independent
- Continuous random variables, probability density
function, cumulative distribution functions, special continuous
(exponential, normal, uniform, Pareto, maybe another one), distribution
sums of random variables, functions of normal random variables. A
bit of joint distribution of two random variables for the discrete and
- Expectation, moments of a random variable, expected value of
random variables with the distributions seen earlier
- Central Limit Theorem (CLT), Law of Large Numbers (LLN).
- Conditional distribution and expectations.
- Brief, very brief mention of stochastic processes, like
queues, Markov models, etc…
- Descriptive Data Analysis of random samples
is a random sample? Examples of samples arising from different
models. Data not coming from random samples. Design of experiments.
- Types of data we encounter: measuring, counting, classifying.
- Sample Histograms and box plots for numerical variables
statistics of a sample: Sample mean, sample median, sample quartiles,
range, range, sample proportion, variance and standard deviation
- Descriptive comparison of two groups
- Scatter plots
- Sample covariance and correlations
- Descriptive regression analysis
- Sampling and back to probability
- Sample statistic
- Independent, dependent and random samples
- The expected value and variance of the sample mean
- The expected value and variance of the sample proportion
- Unbiasedness, precision, accuracy, consistency, efficiency of
- Law of Averages
- Central Limit Theorem for the sample mean
- Central Limit theorem from sample proportion.
- Statistical Inference
- Parameter estimation. Maximum likelihood estimation
- Confidence Intervals for the model mean
- Confidence Intervals for the model proportion
- Hypothesis testing for the model mean
- Hypothesis testing for the model proportion
intervals and hypothesis testing for the difference of two mean and the
for the difference of two proportions.