Introduction to Probability and Statistics Handwritten Notes PDF

Content of this pdf

Theory of probability

Uncertainty

History

Random experiments

Random experiments

Exhaustive events or cases

Favorable events

Identical means

Mathematical or classical or A Prior Probability

Solve questions

Classical  definition

Candidate

Statistical or empirical definition

Classical definition

Limited of statistical

Axiomatic definition

Set theory

Classical limitation

Empirical limitation

Statistical or empirical equation

Subset

Equivalent set

Empty set

Complement

Union

Intersection

Results

De morgan’s law

Generalized De morgan’s law

Union and intersection of two sets

Disjoint or mutually exclusive

sample space

Event

Probability function

Revise

Properties or sigma field

Some theorems of probability

Addition theorem of probability

Boole’s inequality

Conditional probability

Examples

Multiplication theorem of probability for independent events

Pairwise independent events

Mutually independent events

Problems

Law of total probability

Averages of measure of central tendency or measure of location

Requisites for an ideal measure of central tendency

Arithmetic mean

Properties of arithmetic mean

Merits and demerits

Geometric mean

Merits and demerits

Uses

Harmonic mean

Merits and demerits

Median

Examples

Merits and demerits

Mode

Measure of dispersion

Central tendency

Limitation

Interquartile range or Quartile Deviation

Mean deviation

Combined standard deviation

Moments

central moment

Relation between central moment and row moment about point

Effects of change of origin and scale on moments

Sheppard’s correction for moments

Pearson’s coefficient

Factorial moments

Measures of skewness

A relative measure of skewness

Bowles Coefficient of skewness

Coefficient of skewness based on the moment

Kurtosis

Central moment

Coefficient of skewness

Coefficient of kurtosis

Random variable

Types of a random variable

Probability distribution

Distribution of function

Revision

Probability density function

Examples

Two-dimensional random variable

Join probability function

Marginal probability density

Etc.

All topic covers