## STA 130A Mathematical Statistics: Brief Course

**Units:** 4

**Format:**

Lecture: 3 hours

Discussion: 1 hour

**Catalog Description:**

Basic probability, densities and distributions, mean, variance, covariance, Chebyshev's inequality, some special distributions, sampling distributions, central limit theorem and law of large numbers, point estimation, some methods of estimation, interval estimation, confidence intervals for certain quantities, computing sample sizes.

**Prerequisite:** MAT 016C or MAT 017C or MAT 021C

**Summary of course contents:**

- Basic probability
- Random experiments, sample spaces, events
- Elementary rules of probability
- Independence, conditional probability, Bayes Theorem

- Random variables
- Discrete and continuous random variable
- Densities and distributions
- Expectations, mean, variance
- Covariance and conditional expectation for discrete random variables
- Chevyshev's inequality

- Special distributions and models, with applications
- Discrete distributions including binomial, poisson, geometric, negative binomial and hypergeometric
- Continuous distributions including normal, exponential, gamma, uniform
- Special conbinations and relationships:
- Sums of independant binomial, poisson, normal and gamma random variables
- Poisson processes and waiting times

- Bridging statistics and probability
- Sampling distributions
- Special sampling: t, chi-square, F
- Central limit theorem and law of large numbers
- Approximations for certain discrete random variables

- Point estimation
- Minimum variance unbiased estimation, Cramer-Rao inequality
- Maximum likelihood estimation
- Method of moments estimators
- Desirable properties of estimators

- Interval estimation
- The basic idea of a confidence interval
- Confidence intervals for means, proportions and variances
- Computing sample size for desired width

**Restrictions:
** Only 2 units of credit allowed to students who have taken course 131A.

**Illustrative reading:
** None

**GE3:**

SE, QL

**Potential Overlap:**

Statistics 131A and Mathematics 135A cover the topics in the first part of the course but with more in depth and theoretical orientations.

**History:**

None