Math
447, Introduction to Probability and Statistics I
List of topics
BOOK:
Mathematical Statistics with applications, 6th ed, by Dennis D. Wackerly, W. Mendenhall III, R. L. Scheaffer
- Introduction to Statistics
- Introduction to Probability
- Review of set notation
- Discrete probabilities
- The sample point method for finding the probability of an event
- Tools for counting sample points
- Conditional probability
- Independent events
- Laws of probability
- The event decomposition method
for finding the probability of an event
- The total law of probability and Bayes' formula (2.10)
- Random variables
- Probability distribution for a discrete random variable
- Expected value of a random variable or a function of
a random variable
- Binomial distribution
- Geometric distribution
- Negative binomial distribution
- Hypergeometric distribution
- Poisson distribution
- Moments and moments generating functions
for discrete random variables
- Tchebysheffs's inequality for discrete random variables
- Distribution of a continuous random variable
- Expected value of a continuous random variable
- Uniform distribution
- Normal distribution
- Gamma distribution
- Beta distribution
- Moments and moments generating functions for continuous random variables
- Tchebysheffs's inequality for continuous random variables
- Bivariate and multivariate distributions
- Marginal and conditional distributions
- Independent random variables
- Expected value of a function of random variables
- Covariance of two random variables
- Expected value and variance of linear functions of random variables
- Multinomial distribution
- Bivariate normal distribuion
- Conditional expectations
- Finding the density of a function of random variables
- Method of distribution functions
- Method of transformations
- Method of moment generating functions
- Order statistics
- Sampling distributions for normal data
- Central limit theorem