STAT 400 (Applied Probability and Statistics I)
| DESCRIPTION |
Stat 400 is an introductory course to probability, the
mathematical
theory of randomness, and to statistics, the mathematical science of
data
analysis and analysis in the presence of uncertainty. Applications of
statistics
and probability to real world problems are also presented. |
| PREREQUISITES |
Math 141 |
| TOPICS |
Data summary and visualization
Sample mean, median, standard deviation
*Sample quantiles, *box-plots
(Scaled) relative-frequency histograms
Probability
Sample space, events, probability axioms
Probabilities as limiting relative frequencies
Counting techniques, equally likely outcomes
Conditional probability, Bayes' Theorem
Independent events
*Probabilities as betting odds
Discrete Random Variables
Distributions of discrete random variables
Probability mass function, distribution
function
Expected values, moments
Binomial, hypergeometric, geometric, Poisson
distributions
Binomial as limit of hypergeometric
distribution
Poisson as limit of binomial distribution
*Poisson process
Continuous Random Variables
Densities: probability as an integral
Cumulative distribution, expectation, moments
Quantiles for continuous rv's
Uniform, exponential, normal distributions
*Gamma function and gamma distribution
*Other continuous distributions
*Transformation of rv's (by smoothly
invertible
functions): distribution function and density
*Simulation of pseudo-random variables of
specified distribution (by applying inverse dist. func. to a uniform
pseudo-random
variable)
Joint distributions, random sampling
Bivariate rv's, joint (discrete) probability
mass functions
*Expectation of function of jointly
distributed
rv's
*Joint and marginal densities
*Correlation, *covariance
Mutually independent rv's. Mean and variance
of sums of independent rv's
*Sums of rv's, laws of expectation
Law of Large Numbers, Central Limit Theorem
Connection between scaled histograms of random
samples and probability density functions
Point estimation
Populations, statistics, parameters and
sampling
distributions
Characteristics of estimators : consistency,
accuracy as measured by mean square error, *unbiasedness
Use of Central Limit Theorem to approximate
sampling distributions and accuracy of estimators
Method of moments estimator
*Maximum likelihood estimator
*Estimators as population characteristics
of the empirical distribution
Confidence intervals
Large sample confidence intervals for means
and proportions using Central Limit Theorem
*Small sample confidence intervals for normal
populations using Student's t distribution
Confidence interval as decision
procedure/hypothesis
test
Hypothesis Tests
*Hypothesis testing definitions (Null and
alternate hypotheses, Type I and II errors, significance level and
power,
p-values)
*Tests for means and proportions in large
samples, based on the Central Limit Theorem
*Small sample tests for means of normal
populations
using Student's t distribution
*Exact tests for proportions based on binomial
distribution
*optional
|
| LINKS |
Notes
on teaching STAT 400 (internal only)
|
| TEXT |
Text(s)
typically used in this course. |
|
