Instructor: Ivo D. Dinov, Ph.D. Assistant Professor in Statistics, Research Scientist, Department of Neurology, UCLA School of Medicine E-mail:

Teaching Assistant: Neda Farzinnia   E-mail: neda@stat.ucla.edu

Lectures: KNUDSEN 1200B  MWF 8:00 - 8:50 AM MS 5128

Office Hours
• Dr. Dinov: M W F: 10:00 AM - 11:00 AM, or by arrangement
• TA's: Neda Farzinnia TBA
• VOH/Forum 24/7

Tentative schedule of examinations:
• Midterm: Fifth week of classes: Friday, May. 07, 2004 at 8:00 AM,  MS 5128.
• Final: Code: 01 - Thursday, June 17, 2004, 11:30am-2:30pm, MS 5128

Tentative schedule of topics to be covered
1. Introduction - Probability, data analysis, sampling theory and statistical inference.
2. Basic Probability
   
   • Probability models, sample space, events, “some” algebra of events
   • Probability axioms, combinatorial problems, conditional probability, independent events, Bayes’ rule, Bernoulli trials.
   • Discrete random variables, probability mass function, cumulative distribution functions, special discrete distributions (Bernoulli, Binomial, geometric, negative binomial, poisson, hypergeometric, discrete uniform), independent random variables.
   • Continuous random variables, probability density function, cumulative distribution functions, special continuous distributions (exponential, normal, uniform, Pareto, maybe another one), distribution of sums of random variables, functions of normal random variables. A little bit of joint distribution of two random variables for the discrete and continuous case.
   • 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…
   
   
3. Descriptive Data Analysis of random samples
   
   • What is a random sample? Examples of samples arising from different probability 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
   • Descriptive statistics of a sample: Sample mean, sample median, sample quartiles, interquartile range, range, sample proportion, variance and standard deviation
   • Descriptive comparison of two groups
   • Scatter plots
   • Sample covariance and correlations
   • Descriptive regression analysis
   
   
4. 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 estimators
   • Law of Averages
   • Central Limit Theorem for the sample mean
   • Central Limit theorem from sample proportion.
   
   
5. 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
   • Confidence intervals and hypothesis testing for the difference of two mean and the same for the difference of two proportions. 
     

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