Course

Probability and statistics

You will learn to measure uncertainty: events, random variables, distributions and the methods for drawing conclusions from data. It supports evidence-based decisions in science, engineering and finance.

32concepts

6topics

320exercises

≈ 16 hof study approx.

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Course path

1
Probability foundations 6 concepts
Sample space · Event · Probability measure · Classical probability · Addition rule · Permutations and combinations
2
Conditional probability 4 concepts
Conditional probability · Independence of events · Law of total probability · Bayes' theorem
3
Random variables 7 concepts
Random variable · Probability mass function · Probability density function · Cumulative distribution function · Expected value · Variance · Covariance
4
Distributions 6 concepts
Bernoulli distribution · Binomial distribution · Poisson distribution · Uniform distribution · Exponential distribution · Normal distribution
5
Limit theorems 3 concepts
Chebyshev inequality · Law of large numbers · Central limit theorem
6
Statistical inference 6 concepts
Random sample · Sample mean · Estimator · Confidence interval · Hypothesis test · p-value

Sources

Joseph K. Blitzstein, Jessica Hwang, Introduction to Probability, 2nd edition, CRC Press, 2019.
Sheldon Ross, A First Course in Probability, 10th edition, Pearson, 2019.
Larry Wasserman, All of Statistics, 1st edition, Springer, 2004.
Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye, Probabilidad y estadística para ingeniería y ciencias, 9.ª edición, Pearson, 2012.
George Casella, Roger L. Berger, Statistical Inference, 2nd edition, Duxbury / Cengage, 2002.