AL-302 Introduction to Probability and Statistics Notes
5 notes for Introduction to Probability and Statistics, unit by unit.
Notes for AL-302
- Unit 1 · Short notes Basic Probability Probability spaces, conditional probability, independence · Discrete random variables · Independent random variables, the multinomial distribution, Poisson approximation to the binomial distribution, infinite sequences of Bernoulli trials, sums of independent random variables · Expectation of discrete random variables, moments, variance of a sum, correlation coefficient, Chebyshev's inequality
- Unit 2 · Short notes Continuous Probability Distributions Continuous random variables and their properties · Distribution functions and densities · Normal, exponential and gamma densities
- Unit 3 · Short notes Bivariate Distributions Bivariate distributions and their properties · Distribution of sums and quotients · Conditional densities · Bayes' rule
- Unit 4 · Short notes Basic Statistics Measures of central tendency: moments, skewness and kurtosis · Probability distributions: binomial, Poisson and normal – evaluation of statistical parameters for these three distributions · Correlation and regression – rank correlation
- Unit 5 · Short notes Applied Statistics Curve fitting by the method of least squares – fitting of straight lines, second‑degree parabolas and more general curves · Test of significance: large‑sample test for single proportion, difference of proportions, single mean, difference of means, and difference of standard deviations
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