Probability

Textbook

• R. E. Walpole, R. H. Myers, S. L. Myers and K. Ye, "Probability & Statistics for engineers & scientists", 7/e, Prentice Hall, 2002 (東華代理)

Reference Books

• H. Stark and J. Woods, "Probability and random processes with applications to signal processing", 3/e, Prentice Hall, 2002(台北代理)

•  A.Papoulis, “Probability, Random Variables and Stochastic Processes”, 2002, McGraw-Hill (歐亞代理)

• R. D. Yates and D. J. Goodman, "Probability and stochastic processes", 2/e, Wiley, 2005 (滄海代理)

Score

• Homework and Programming (30%)

• Midterm Examination (30%)

• Final Examination (40%)

Contents

• 1. Introduction to Probability
  1.1 Combinations
  1.2 What is a Probability?

• 2. Probability
  2.1 Sample Spaces
  2.2 Sets in probability theory
  2.3 Counting sample points
  2.4 Probability of an event
  2.5 Additive Rules
  2.6 Conditional probability and Independent
  2.7 Multiplicative Rules
  2.8 Bayes’Theorem

• 3. Random Variables and Probability Distributions
  3.1 Concept of a random variable
  3.2 Discrete probability distributions
  3.3 Continuous probability distributions
  3.4 Conditional distributions
  3.5 Joint probability distributions

• 4. Mathematical Expectation
  4.1 Mean of a Random Variable
  4.2 Variance and Covariance
  4.3 Means and Variances of Linear Combinations of Random Variables
  4.4 Conditional expectations
  4.5 Chebyshev and Schwarz inequalities
  4.6 Information Theory

• 5. Some Discrete Probability Distributions
  5.1 Discrete Uniform Distribution
  5.2 Binomial and Multinomial Distributions
  5.3 Hypergeometric Distribution
  5.4 Negative Binomial and Geometric Distributions
  5.5 Poisson Distribution and the Poisson Process
  5.6 Relationship between discrete distribution
  5.7 Other discrete distribution

• 6. Some Continuous Probability Distributions
  6.1 Continuous Uniform Distribution
  6.2 Normal Distribution
  6.3 Gamma and Exponential Distributions
  6.4 Chi-Squared Distribution
  6.5 Lognormal Distribution
  6.6 Weibull Distribution
  6.7 Reliability and Failure rate function
  6.8 Other Distribution

• 7. Functions of Random Variables (FRV) and Vector Random Variables
  7.1 Transformations of Variables
  7.2 Solving problems of the type
  7.3 multi-dimensional random variables
  7.4 Multiple transformation of random variables
  7.5 Expectation vectors and covariance matrices
  7.6 Multidimensional Gaussian Law
  7.7 Moments and Moment-Generating Functions
  7.8 Joint Moment-Generating Functions
  7.9 Characteristic function

• 8. Fundamental Sampling Distributions and Data Descriptions
  8.1 Random Sampling
  8.2 Some Important Statistics
  8.4 Sampling Distributions
  8.5 Sampling Distribution of Means
  8.6 Sampling Distribution of S2
  8.7 t-Distribution
  8.8 F-Distribution
  F-Distribution

歷屆考題

1. 2004年