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Ivo Dinov
UCLA Statistics, Neurology, LONI

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Statistics 110A
Spring 2004

Probability and Statistics for Engineers I

Textbokk & Coverage

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

Teaching Assistants:

TBA (section 1a,b) E-mail: zmdl@stat.ucla.edu

TBA (section 1c) E-mail: chea@stat.ucla.edu

Textbook: Probability and Statistics for Engineering and the Sciences (2004), Sixth Edition by Jay L. Devore, Published by Brooks/Cole.

Tentative schedule of topics to be covered

Introduction - Probability, data analysis, sampling theory and statistical inference.
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…
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
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.
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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Statistics 110ASpring 2004

Probability and Statistics for Engineers I

Statistics 110A
Spring 2004