Probability and Statistics

Books that cover Section 1

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Probability & Statistics for Data Science

B.Tech AI & Data Science, Semester 3 · Dr. D.C. Agarwal, Dr. Pradeep K. Joshi

Covers: Most of the section — Bayes theorem and conditional probability, moment generating functions, the binomial, Poisson and normal distributions, correlation and regression, and hypothesis testing with the t-, F-, chi-square and z-tests.

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Introduction to Probability & Statistics

B.Tech AIML & CS/DS, Semester 3 · Dr. D.C. Agarwal, Dr. Pradeep K. Joshi

Covers: Probability spaces and conditional probability, Bernoulli trials and Chebyshev’s inequality, the normal, exponential and gamma densities, Bayes’ rule, and the large- and small-sample significance tests (t, chi-square).

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Statistical Mathematics (MCA)

MCA 1st Semester · Dr. D.C. Agarwal, Dr. Pradeep K. Joshi

Covers: Probability axioms and conditional probability, PMF/PDF and the binomial, Poisson and normal distributions, and testing of hypotheses with the t-, chi-square and F-distributions.

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Full syllabus — Section 1

• Counting (permutations and combinations); probability axioms; sample space, events, independent events, mutually exclusive events; marginal, conditional and joint probability; Bayes theorem
• Conditional expectation and variance; mean, median, mode and standard deviation; correlation and covariance
• Random variables; discrete random variables and probability mass functions — uniform, Bernoulli, binomial; continuous random variables and probability distribution functions — uniform, exponential, Poisson, normal, standard normal, t-distribution, chi-squared
• Cumulative distribution function; conditional PDF; central limit theorem; confidence interval; z-test, t-test, chi-squared test