Probability theory plays an essential role in engineering design, safety analysis, and decision making throughout our culture. Statistics plays the key role of bridging probability models to the real world. Probability and statistics are becoming very popular, both at the college and at the high school level.
This introduction course will cover the general conceptions and methods about probability and statistics. The main topics include basic probability concepts, one or more random variables and their distributions, expectations and moments of random variables, the law of large numbers and central limit theorems, sampling distributions, parameter estimatiion and hypothesis testing.
Upon completion of this course, you can gain terminology, classifications and methods of probability and statistics and you will:
1) know the basic axioms and set theory upon which probability theory is based
2) solve problems by counting probabilities by means of properties and some important fomula( conditional probability, independence, and Bayes theorem)
3) understand the concept of random variables and describe their probability distributions by cdf, pmf, or pdf
4) understand joint, marginal, and conditional distributions
5) grasp several important discrete or continuous random variables (Bernoulli distribution, binomial distribution, Poinsson distribution, Hypergeometric distribution, Uniform distribution, Exponential distribution, Normal distribution and etc), and know when to use them
6) determine the distribution of a general function of one or more random variables
7) understand and find the mean and variance of a random variable
8) understand and find covariance and correlation of two random variables
9) be able to apply the theory of expectation to solve decision problems involving the maximization of expected return
10) know and understand the law of large numbers, the central limit theorem and how to use them in practice
11) grasp some numerial and graphical methods to explore data
12) know various well-known smapling distributions and how they are used in inferential statistics
13) grasp two types of estimation techniques (method of moments and maximum likelihood estimate)
14) know several criteria for the point estimator
15) understand confidence intervals
16) construct confidence intervals for parameters of one or two normal populations
17) understand basic thoughts of hypothesis testing
18) test hypotheses about parameters concerning one or two normal populations
