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
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