Covariance Explained: Change of Origin vs. Scale Made Simple! Welcome to PostNetwork Academy’s Data Science and AI Lecture Series! In this post, we’ll explore the mathematical concept of covariance and how it behaves under changes of origin and scale. Let’s break it down step by step. Theorem: Covariance Independence We aim to prove that: Covariance […]
Covariance Explained: Change of Origin vs. Scale Made Simple! Read More »
Introduction Welcome to the Data Science and A.I. Lecture Series presented by PostNetwork Academy. In this session, we’ll focus on key statistical concepts: moments about the mean, skewness, and kurtosis. These concepts are essential in understanding data distribution characteristics and play a significant role in data science, artificial intelligence, and statistical analysis. In this
Moments and Pearson’s Coefficient Simplified | Data Science & A.I. Lecture Series Read More »
Before understanding Binomial distribution you have to understand Bernoulli trial. What is Bernoulli trial? A Bernoulli trial is a random experiment in which there are two possible outcomes failure and success getting head when tossing a coin is success and getting tail is failure getting 4 is success when rolling a dice and failure when
Understand Binomial Distribution Read More »
Variance and Standard Deviation are both essential concepts in statistics and finance. Let’s explore the differences between them: Variance: Definition: Variance is a numerical value that describes the variability of observations from their arithmetic mean. Calculation: To find the variance, calculate the squared differences between each data point and the mean, then average these squared
Variance and Standard Deviation Read More »
Suppose you want to solve an equation x2+1=0 then you will get x=√-1 which does not belongs to real number system. Leonhard Euler proposed to write √-1 as i (iota) and gave concept of complex numbers. Integral Power of i (iota) i2=-1, i3=-i, i4=1 i5=i, i6=-1, i7=-1, i8=1
Complex Numbers in Mathematics Read More »
Random variable is a very important concept in probability, statistics, data science and machine learning, one must learn concept of random variable and related concepts. In this post, I have explained random variable and probability mass function that will help you to have basic understanding of random variable and probability mass function. To understand random
Random Variable and Probability Mass Function Read More »
Example-1- Write the solution set of the equation x2+x-2=0. Solution- x2-x+2x-2=0 x(x-1)+ 2(x-1)=0 (x-1)(x+2)=0 x=1 , x= – 2 S={1, -2} Example-2- Write the set {x: x is a positive integer and x2<40} Solution- S={1, 2, 3, 4, 5, 6} 7, 8, 9, 10, ………… can not be included because their squares are greater than
Tabular (Roster) Form and Set-Builder Form Read More »
In real life, we often come across collection of objects viz. #Cricket Team #Pack of Cards #Members of a Club In mathematics, we also come across collections, examples are. #Odd natural numbers #Even natural numbers #Numbers which is divisible by 3 and less than 20. If you observe each example is well-defined collection of objects.
Sets in Mathematics Read More »