MATHEMATICS - 2(Probability and Statistics)

Basic Probability: Unit: 1
Probability is a measure of the likelihood that a particular event will occur. It is a fundamental concept in discrete mathematics and is used extensively in fields like statistics, computer science, and various branches of science and engineering.

Probability Spaces

29:32
Conditional probability

06:22
Discrete Random Variables and Independent Random Variables

22:14
Multinomial Distribution

14:13
Poisson Approximation to the binomial Distribution

08:01
Infinite Sequences of Bernoulli trials

11:04
Expectation of Discrete Random Variables and Moments

44:12
Variance of a Sum

05:36
Chebyshev’s Inequality

11:12

Continuous Probability Distributions: Unit: 2
In discrete mathematics, continuous probability distributions deal with variables that can take on an infinite number of values within a given range. These distributions are essential for modeling phenomena where outcomes are not restricted to distinct points but rather form a continuum

Bivariate Distributions: Unit: 2
In discrete mathematics, bivariate distributions describe the probability distribution of two discrete random variables. These distributions are essential for understanding the joint behavior of two variables and for solving problems involving probabilities in multivariate settings 1. Joint Probability Mass Function (PMF) 2.Marginal Distributions 3. Conditional Distributions

Basic Statistics: Unit 3
Discrete mathematics deals with structures that are fundamentally discrete rather than continuous. In statistics, this involves the study of countable, distinct values. Key concepts in discrete statistics include measures of central tendency, dispersion, and the use of probability distributions.

Applied Statistics and Small Samples: Unit 4
Applied statistics plays a significant role in discrete mathematics, which focuses on distinct and separate values rather than continuous ones.

Curve fitting by the method of least squares – fitting of straight

27:28
Second order Parabolas and more general curves

14:58
Test of significance: Large sample test for single proportion

42:14
Difference of proportions

17:50
Difference of Single means

24:49
Difference of Standard derivation

12:55
Test for single means

24:16
Difference of means and correlation coefficient

08:15
Test for ratio of variances

10:40
Chi – Square test for goodness of fit and independence of attributes

27:57

Course Content

Basic Probability: Unit: 1 Probability is a measure of the likelihood that a particular event will occur. It is a fundamental concept in discrete mathematics and is used extensively in fields like statistics, computer science, and various branches of science and engineering.

Probability Spaces

Conditional probability

Discrete Random Variables and Independent Random Variables

Multinomial Distribution

Poisson Approximation to the binomial Distribution

Infinite Sequences of Bernoulli trials

Expectation of Discrete Random Variables and Moments

Variance of a Sum

Chebyshev’s Inequality

Continuous Random Variable and properties

Distribution Functions and Densities

Distribution Functions and Normal

Exponential and gamma Densities

Bivariate Distributions and properties

Distribution of Sums and Quotient

Conditional Densities

Baye’s Rule

Measures of Central tendency: Moments, Skewness and Kurtosis

Probability distributions: Binomial , poisson and Normal – Evaluation of statistical parameters for these three distributions:

Correlation

Regression

Rank of Correlation

Applied Statistics and Small Samples: Unit 4 Applied statistics plays a significant role in discrete mathematics, which focuses on distinct and separate values rather than continuous ones.

Curve fitting by the method of least squares – fitting of straight

Second order Parabolas and more general curves

Test of significance: Large sample test for single proportion

Difference of proportions

Difference of Single means

Difference of Standard derivation

Test for single means

Difference of means and correlation coefficient

Test for ratio of variances

Chi – Square test for goodness of fit and independence of attributes

Student Ratings & Reviews

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Basic Probability: Unit: 1
Probability is a measure of the likelihood that a particular event will occur. It is a fundamental concept in discrete mathematics and is used extensively in fields like statistics, computer science, and various branches of science and engineering.

Applied Statistics and Small Samples: Unit 4
Applied statistics plays a significant role in discrete mathematics, which focuses on distinct and separate values rather than continuous ones.