Random Variables And Probability Distributions

Random Variables - Probability distributions - Binomial, Geometric, Normal and Standard normal distributions

What you'll learn

Introduction to random variables ,

Introduction to discrete & continuous probability distributions

Binomial & Geometric distributions

normal & standard normal distributions

Requirements

An optional section is made available as part of section 4 in oder to help those understand the following prerequisites -Fairly good understanding on the essential concepts on Probability including Chance experiments, Sample space, Events, properties involving probability including conditional probability, Bayes theorem etc.

Description

The first section focuses onProbability distributions Starts with identifying the difference between a variable and a random variable. Explains discrete and continuous random variables and their characteristics. Move on to explain the need for the probability distributions. explains the basics, characteristics and definitions around the discrete probability distribution and continuous probability distributions. explains the graphical representations of probability distributions involving histograms and continuous functions Every aspect is illustrated with a simple case study to appreciate the detailsThe second section focusses ontwo important discrete probability distributions namely Binomial distribution & Geometric distribution Explains - the conditions to be met for each of these experiments - derivation of mathematical functions that describe these distributions - mean and standard deviation (variance) for each of these distributions - applications of these distributions in certain real world using examplesThe third section explains What is a Normal distribution? What is a standard Normal distribution ( z value / z curve )? How are probabilities evaluated for a standard Normal distribution and normal distribution? How to judge if a sample data is Normally distributed? What is a normal probability plot? How to transform data into a normal distribution when the sample is not? How to arrive at probabilities for a discrete probability distribution using normal approximations?Section four is only for reference and is OPTIONALAdded here in order to help those who do not have the pre-requisite knowledge on essential concepts on probabilityExplains the basic underlying concepts and definitions on probability involving, Chance experiments, Sample Space, Events, LikelihoodTwo important theorems on probability namely- Conditional probability and- Bayes theoremVarious properties on Probability

Overview

Section 1: Random Variables and introduction to Probability distributions

Lecture 1 Random variables and Probability distributions

Section 2: Binomial & Geometric distributions

Lecture 2 Binomial & Geometric distributions

Section 3: Normal & Standard normal distributions

Lecture 3 Normal & Standard normal distributions

Section 4: (OPTIONAL) Essential concepts on probability - a pre-requisite

Lecture 4 Probability: Basic concepts and definitions

Lecture 5 Conditional probability

Lecture 6 Bayes Theorem

Lecture 7 Probability: Basic properties, rules and definitions

This course is one among the essential concepts on Probability and Statistics that an aspiring Data Scientist .