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Essentials Of Data Science With R Software - 1: Probability And Statistical Inference

Dr. Shalabh

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Any data analysis is incomplete without statistics. After getting the data, the statistical tools aims to extract the information hidden inside the data. The main objective of statistics is to work on a small sample of data but provide conclusions for the whole population. Such results cannot be obtained without learning the concepts and tools of theory of probability and statistical inference. With the advent of data science, it has become important to learn those tools from computational and data based aspects. Without learning the basic fundamentals of probability theory and statistical inference, it is difficult to implement them correctly on the data and draw correct statistical conclusions.

Lecture 01: Data Science- Why, What, and How?

Lecture 02: Installation and Working with R

Lecture 03: Installation and Working with R Studio

Lecture 04: Calculations with R as a Calculator

Lecture 05: Calculations with Data Vectors

Lecture 06: Built-in Commands and Bivariate Plots

Lecture 07: Logical Operators and Selection of Sample

Lecture 8: Introduction to Probability

Lecture 9: Sample Space and Events

Lecture 10: Set Theory and Events using Venn Diagrams

Lecture 11: Relative Frequency and Probability

Lecture 12: Probability and Relative Frequency - An Example

Lecture 13: Axiomatic Definition of Probability

Lecture 14: Some Rules of Probability

Lecture 15: Basic Principles of Counting- Ordered Set, Unordered Set, and Permutations

Lecture 16: Basic Principles of Counting- Combination

Lecture 17: Conditional Probability

Lecture 18: Multiplication Theorem of Probability

Lecture 19: Bayes' Theorem

Lecture 20: Independent Events

Lecture 21: Computation of Probability using R

Lecture 22: Random Variables - Discrete and Continuous

Lecture 23: Cumulative Distribution and Probability Density Function

Lecture 24: Discrete Random Variables, Probability Mass Function and Cumulative Distribution Function

Lecture 25: Expectation of Variables

Lecture 26: Moments and Variance

Lecture 27: Data Based Moments and Variance in R Software

Lecture 28: Skewness and Kurtosis

Lecture 29: Quantiles and Tschebyschev's Inequality

Lecture 30: Degenerate and Discrete Uniform Distributions

Lecture 31: Discrete Uniform Distribution in R

Lecture 32: Bernoulli and Binomial Distribution

Lecture 33: Binomial Distribution in R

Lecture 34: Poisson Distribution

Lecture 35: Poisson Distribution in R

Lecture 36: Geometric Distribution

Lecture 37: Geometric Distribution in R

Lecture 38: Continuous Random Variables and Uniform Distribution

Lecture 39: Normal Distribution

Lecture 40: Normal Distribution in R

Lecture 41: Normal Distribution - More Results

Lecture 42: Exponential Distribution

Lecture 43: Bivariate Probability Distribution for Discrete Random Variables

Lecture 44: Bivariate Probability Distribution in R Software

Lecture 45: Bivariate Probability Distribution for Continuous Random Variables

Lecture 46: Examples in Bivariate Probability Distribution Functions

Lecture 47: Covariance and Correlation

Lecture 48: Covariance and Correlation - Examples and R Software

Lecture 49: Bivariate Normal Distribution

Lecture 50: Chi square Distribution

Lecture 51: t - Distribution

Lecture 52: F - Distribution

Lecture 53: Distribution of Sample Mean, Convergence in Probability and Weak Law of Large Numbers

Lecture 54: Central Limit Theorem

Lecture 55: Needs for Drawing Statistical Inferences

Lecture 56: Unbiased Estimators

Lecture 57: Efficiency of Estimators

Lecture 58: CramÃ©r-Rao Lower Bound and Efficiency of Estimators

Lecture 59: Consistency and Sufficiency of Estimators

Lecture 60: Method of Moments

Lecture 61: Method of Maximum Likelihood and Rao Blackwell Theorem

Lecture 62: Basic Concepts of Confidence Interval Estimation

Lecture 63: Confidence Interval for Mean in One Sample with Known Variance

Lecture 64: Confidence Interval for Mean and Variance

Lecture 65: Basics of Tests of Hypothesis and Decision Rules

Lecture 66: Test Procedures for One Sample Test for Mean with Known Variance

Lecture 67: One Sample Test for Mean with Unknown Variance

Lecture 68: Two Sample Test for Mean with Known and Unknown Variances

Lecture 69: Test of Hypothesis for Variance in One and Two Samples

Live Session 01-04-2021

Live Session 03-12-2022

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Course Duration

37 h 8 m 58 s
Course Level

Intermediate
Student Enrolled

159
Language

English

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37 h 8 m 58 s Video Lectures
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