• Probability and Statistics
    • Department of Mathematics
    • Credit. 2.5
    • MA119
    • Enroll
    • WILL BEGIN
    • Fall , 2015
    • 2418
    • Course Description:
    • ( Exchange Programme )
    • Probability and statistics is a mathematical discipline which studies stochastic phenomena. Now it is widely used in industrial and agricultural production, science and technologies. This course is one of the important basic courses for engineering majors in comprehensive universities, through which students shall know the general conceptions and methods about probability and statistics, master the basic definitions, theories and corresponding methods, master the methods to deal with random phenomenon by means of establishing the basic statistical models and master the necessary ability in English listening, speaking and so on. We stress theory and practice combined, in order to help students promote their ability of applying statistical methods in their daily life and scientific research.
    • Course Syllabus:
    • After completing the course, students should understand and master:
      1.The concept of random events, the relationship between events and calculations related. The calculation laws for probabilities.
      2.The concept and the properties of conditional probability. Methods to solve probability problems by multiplication rule, total probability formula and Bayes' Rule. The concept of independent events. Methods to solve probability problems by the independence of the events.
      3.The concept and the properties of conditional probability. Methods to solve probability problems by multiplication rule, total probability formula and Bayes' Rule. The concept of independent events. Methods to solve probability problems by the independence of the events.
      4.Multidimensional random variables. Two dimensional random variables. Bivariate distributions, marginal distributions and conditional distributions. The concepts and properties of cumulative distribution function (cdf) and probability density function (pdf) of continuous distributions, random variable independency, the distribution of functions with respect to random variables. Master the methods to solve the distribution of the function of independent random variables.
      5.The definitions, properties and calculations of expectation and variance. Expectation and variance of Binomial distribution, Poisson distribution, Uniform distribution, Exponential distribution and Normal distribution. The definition, properties and calculations of covariance and correlation coefficient.
      6.The Chebyshev's Inequality. Bernoulli's Law of Large Numbers, Chehyshev's Law of Large Numbers, the Central Limit Theorem. To estimate the probability of the random events by the Chebyshev's Inequality or the Central Limit theorem.
      7.The concepts of population, individual, statistic and its distribution. The Chi-Square distribution,the t distribution,the F distribution. The distributions of statistics frequently used from normal population.
      8.Parametric estimation with the method of moment and the method of maximum likelihood. Efficiency of estimations. The interval estimation of the parameter of the normal distribution.
      9.The basic idea and definition of testing hypotheses. The testing methods for expectation and variance of the normal population.
    • Schedule:
    • Topics/ Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1.Random events and probability /4 Credit Hours/lecture in the classroom with ppt/ Written assignment/ master concepts, do all hw./Check and correct hw
      2.Conditional probability/4 Credit Hours /lecture in the classroom with ppt/Written assignment/ master concepts, do all hw./ Check and correct hw
      3.Random variables and their distributions/8 Credit Hours /lecture in the classroom with ppt/ Written assignment/master concepts, do all hw./Check and correct hw
      4.Multidimensional random variables and distribution/6 Credit Hours /lecture in the classroom with ppt/ Written assignment/master concepts, do all hw./Check and correct hw
      5.Numerical Characteristis/ 6 Credit Hours /lecture in the classroom with ppt/Written assignment/ master concepts, do all hw./ Check and correct hw
      6.The law of large numbers and the Central Limit Theorem/4 Credit Hours /lecture in the classroom with ppt/ Written assignment/master concepts, do all hw./ Check and correct hw
      7.Basic concepts of mathematical statistics/6 Credit Hours /lecture in the classroom with ppt/ Written assignment/master concepts, do all hw./ Check and correct hw
      8.Parameter estimation/6 Credit Hours /lecture in the classroom with ppt/ Written assignment/ master concepts,do all hw./ Check and correct hw
      9. Testing Hypotheses/4 Credit Hours /lecture in the classroom with ppt/ Written assignment/ master concepts, do all hw./
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • Qiu Lin
    • Associate Professor
    • Read more
    • Female
    • E-mail:
    • linqiu@sjtu.edu.cn
    • Profile
    • April ,1998- March,2001,Graduate School of Human Informatics,Nagoya University, Japan PhD
      April, 2001- March, 2003, Postdoctoral fellow of Japan Society for the Promotion of Science (JSPS)
      May, 2003 until now, department of mathematics, SJTU
      Numerical analysis and its application to mathematical modelling. Aiming the application and development towards computational science and engineering as well as mathematical modelling, the research of numerical algorithms for systems of ordinary differential Current research topics are:
      1. Discrete variable solution of delay-differential equations and its stability
      2. Numerical analysis of dynamics systems
      3. Applied mathematics and scientific/engineering computing
      4. Numerical methods for singular perturbation systems and others relevant to the above.
  • Prerequisite Course:

    Calculus, Linear Algebra

  • Textbooks:

    1. Morris H.DeGroot ,Mark J.Schervish, Probability and Statistics ( fourth edition),China Machine Press, 2012
    2. Jay.L. Devore, Probability and Statistics, 5th ed. Higher Education Press, 2010
    3. H. Jeffreys, Theory of Probability, 3rd ed. Oxford: Oxford University Press, 1998
    4. J.T. McClave, T. Sincich, A First Course in Statistics, 7th ed. Upper Saddle River, NJ: Prentice Hall; London: Pre
  • Grading:

    80%/finial exam
    20%/assignment
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