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Probability and Statistics (06_XBSTA) ​

  • Coefficient : 2
  • Hourly Volume: 51.0h (including 27.0h supervised)
    CTD : 18h supervised
    Labo : 9h supervised
    Out-of-schedule personal work : 24h

AATs Lists

Description ​

  1. Probability:
  • Discrete and continuous random variables,
  • Common distributions (uniform, Bernoulli, binomial, Poisson, normal, exponential),
  • Calculations of expectations, variances,
  • Functions of random variables,
  • Independent random variables,
  • Conditional probabilities,
  • Asymptotic behavior (law of large numbers).
  1. Statistics:
  • Sampling concepts,
  • Estimators,
  • Statistical tests.

Learning Outcomes (AAv) ​

  • AAv1 [hours: 25, B1, B2, B3]: By the end of this course, each student will be able to complete a problem of parametric estimation both as point estimation and within a confidence interval in the context of sampling.

    • Specifically:
      • The student can discuss the quality of an estimator;
      • The student can find classic estimators in the context of sampling (Mean, Variance, Proportion);
      • The student can implement the maximum likelihood method;
      • The student knows and can use the distributions applied in the estimation of small Gaussian samples;
      • The student can use the Central Limit Theorem to explain the distributions used in the estimation of large samples and apply these distributions;
      • The student can carry out confidence interval estimation in the context of sampling and illustrate the method.

  • AAv2 [hours: 26, B1, B2, B3]: By the end of this course, each student will be able to conduct a hypothesis test (tests of independence, fit to a distribution, proportion, mean, and variance).

    • Specifically:
      • The student can conduct a test of independence;
      • The student can conduct a goodness-of-fit test;
      • The student can conduct a proportion test;
      • The student can conduct tests for the mean and variance;
      • The student can determine the critical regions.

Assessment Methods ​

One long continuous assessment (coefficient 1), average of several short continuous assessments in CTD (coefficient 1) and in LAB (coefficient 1).

Keywords ​

Random variables, expectation, variance, standard deviation, sample, statistical tests

Prerequisites ​

Integral calculus (see S2 and S4 programs)

Resources ​