University of California, Irvine
|Week |Chapter |Topics |
| | | |
|1 |6 |JOINTLY DISTRIBUTED RANDOM VARIABLES: Joint PMF’s, PDF’s, joint continuity, marginal distributions, examples, |
| | |multinomial distributions |
| | | |
|2 |6 (cont.) |INDEPENDENT RANDOM VARIABLES: Examples, Poisson together with binomial is Poisson with different mean, symmetry |
| | |characterization of normal distributions, characterization of independence in terms of separation of variables, |
| | |half-lives. |
| | | |
|3 |6 (cont.) |SUMS OF INDEPENDENT RANDOM VARIABLES, convolutions, sums of uniform, Gamma, Normal, lognormal rv’s, Poisson and |
| | |binomial, rv’s. |
| | | |
|4 |6 (cont.) |CONDITIONAL DISTRIBUTIONS. Discrete case, Continuous case, Examples: t-distribution, Chi-squared, bivariate normal, |
| | |distribution of the range of a random sample. joint pdf’s of functions of more than one random variable. |
| | | |
|5 |7 |PROPERTIES OF EXPECATION: Expectation of sums, estimators, sample mean vs. expected value, examples: binomial, |
| | |hypergeometric. MIDTERM. |
| | | |
|6 |7 (cont.) |PROPERTIES OF EXPECTATION (cont.), MOMENTS. Expected numbers of runs, Using indicator functions for counting: unions |
| | |of events and inclusion/exclusion, maximum-minimums identity, Moments of number of events. |
| | | |
|7 |7 (cont.) |MOMENTS (cont.), VARIANCE, COVARIANCE, CORRELATION: Examples of moment calculations: binomial, hypergeometric, negative|
| | |hypergeometric, Variance, Covariance: independent RV’s, variance and covariance of sums. |
| | | |
|8 |7 (cont.) |CONDITIONAL EXPECTATIONS: Conditional expectations as a method for computing probabilities, examples: geometric |
| | |distribution, conditional variance and covariance, prediction using conditional expectations. |
| | | |
|9 |7 - 8 |MOMENT GENERATING FUNCTIONS, MULTIVARIATE GAUSSIANS, LIMIT THEOREMS: Computations of moment generating functions, |
| | |descriptions of multivariate Gaussians using covariance matrices, correlations, Matlab visualizations. Markov and |
| | |Chebyshev inequalities. |
| | | |
|10 |8 (cont.) |LIMIT THEOREMS: Weak and strong laws of large numbers, Central Limit theorem, Other inequalities. |
MATH 130B– Suggested Syllabus
Textbook: A First Course in Probability, by S. Ross
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- university of california irvine related people
- university of california irvine staff
- university of california irvine employment
- university of california irvine address
- university of california irvine online
- university of california irvine employment opportunities
- university of california irvine careers
- university of california irvine medical center careers
- university of california irvine faculty
- university of california irvine website
- university of california irvine jobs
- university of california irvine athletics