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Summer Course in Computational Engineering: Introduction to Probability and Statistics for Engineers

Stanford University Summer Session
8 weeks
Full time
Summer / Short course
Stanford
English

Program description

Summer Course in Computational Engineering: Introduction to Probability and Statistics for Engineers

Random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables.

Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields.

Course Details

  • Intensive Study: Data Science
  • Online Format: Both Synchronous & Asynchronous - This course is taught through a combination of synchronous and asynchronous opportunities.

Admission requirements

  • Be at least 18 years of age by the start of the study abroad program
  • Have graduated from high school or secondary school or equivalent
  • Be able to verify fluency in the English language, using one of the methods described in the English Language Proficiency below
  • Internet-Based Test of English as a Foreign Language (iBT TOEFL) Minimum score of 95 for the iBT TOEFL, International English Language Testing System: Academic (IELTS: Academic) Minimum overall band score of 7.0, or Cambridge Assessment English Minimum score of 180 on the Cambridge English Advanced, CEFR Level C1.

This program is suitable for undergrad/grad students. 


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Program content

Introduction to Probability

  • Sample spaces, events, outcomes, axioms of probability
  • Counting, permutations, combinations, binomial coefficients
  • Probability, conditional probability, Bayes rule, independence
  • Random variables, discrete and continuous distributions
  • Expectation, moments of a distribution
  • Chebyshev’s inequality, characteristic functions, transformations of randomvariables
  • Binomial, Poisson, uniform, and normal distributions
  • Normal approximation to the binomial distribution, examples
  • Exponential distribution, reliability, redundancy
  • Distributions of several random variables, moments of joint distributions,independence, covariance, correlation coefficient

Mathematical Statistics

  • Random sampling, parameter estimation, distribution of the sample mean, centrallimit theorem
  • Confidence intervals for the mean with known variance, sample variance, biasedand unbiased estimators
  • Chi­squared distribution, confidence intervals for the variance, t­distribution,confidence intervals for the mean for small samples
  • Maximum -­likelihood estimation, hypothesis testing
  • Detection, significance levels, test for the mean of a normal distribution with knownvariance, operating curves
  • Test for the mean of a normal distribution with unknown variance, testing aproportion
  • Test for the variance of a normal distribution, test for the difference of two means,non­parametric tests: sign test, test for arbitrary trends
  • Chi­squared test for the goodness of fit
  • Regression analysis
  • Correlation analysis

Tuition fees

The fees for this course is USD 4,700.

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About this institute

Stanford Summer Session

Stanford University Summer Session invites visiting undergraduate, graduate, and high school students to experience Stanford University during its fourth academic quarter. During the eight-week course, Summer Session students are enrolled in the same courses as matriculated Stanford students, and earn...


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Contact info

Stanford University Summer Session

415 Broadway
Academy Hall, Floor 2, 8853
94063 Redwood City California
United States of America

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