The Rise of Generative AI: Overview Unlike traditional AI systems that rely on predefined rules, generative AI models use vast datasets and deep learning techniques to generate novel and contextually relevant outputs. This transformative capability is reshaping industries such as content creation, education, healthcare, and entertainment. How Generative AI Works At its core, generative […]
What is Generative AI? Read More »
Introduction to Machine Learning Definition and Types Welcome to this detailed introduction to Machine Learning. This post explores the fundamental definitions, types of machine learning, and their mathematical representations. What is Machine Learning? What is Machine Learning? What are the different types of Machine Learning? How can we mathematically define each type? Definition of Machine
Introduction to Machine Learning Read More »
Some Questions Based on Continuous Probability Distributions Question Compute the conditional probability: \[ P\left(X > \frac{3}{4} \mid X > \frac{1}{2}\right) \] Theory Behind Solution The conditional probability formula: \[ P(A | B) = \frac{P(A \cap B)}{P(B)} \] For continuous random variables, probability is computed using integration. Understanding Probability Density Functions A probability density function (p.d.f.)
Central Limit Theorem (CLT) and Uniformly Minimum Variance Unbiased Estimator (UMVUE) By: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Question 1 Suppose \( X_1, X_2, \dots \) is an i.i.d. sequence of random variables with common variance \( \sigma^2 > 0 \). Define: \[ Y_n = \frac{1}{n} \sum_{i=1}^{n} X_{2i-1}, \quad Z_n = \frac{1}{n} \sum_{i=1}^{n} X_{2i} \]
Central Limit Theorem (CLT) and Uniformly Minimum Variance Unbiased Estimator (UMVUE) Read More »
Continuous Random Variable and Probability Density Function Data Science and A.I. Lecture Series Continuous Random Variable and Probability Density Function A random variable is continuous if it can take any real value within a given range. Instead of probability mass function, we use probability density function (PDF), denoted by \( f(x) \). The probability
Continuous Random Variable and Probability Density Function Read More »
Some Questions Based on Discrete Probability Distributions Data Science and A.I. Lecture Series Problem 1 2 bad articles are mixed with 5 good ones. Find the probability distribution of the number of bad articles if 2 articles are drawn at random. Let \( X \) be the number of bad articles drawn. Possible values:
Some Questions Based on Discrete Probability Distributions Read More »
Discrete Random Variable and Probability Mass Function Data Science and A.I. Lecture Series A random variable is said to be discrete if it has either a finite or a countable number of values. Countable values are those which can be arranged in a sequence, corresponding to natural numbers. Example: Number of students present each
Discrete Random Variable and Probability Mass Function Read More »
Random Variables and Probability Distributions Introduction to Random Variables In many experiments, we are interested in a numerical characteristic associated with outcomes of a random experiment. A random variable (RV) is a function that assigns a numerical value to each outcome of a random experiment. Example: Consider tossing a fair die twice and defining \(
Random Variables and Probability Distributions Read More »
Bayes’ Theorem and Examples Formula The formula for Bayes’ Theorem is given by: $$ P(E_i | A) = \frac{P(E_i) P(A | E_i)}{\sum_{j=1}^{n} P(E_j) P(A | E_j)} $$ Key Terminology \(E_i\) are hypotheses or possible causes. \(P(E_i)\) is the prior probability of \(E_i\). \(P(E_i | A)\) is the posterior probability of \(E_i\). The denominator ensures
Bayes’ Theorem and Examples | Data Science & AI Read More »
Law of Total Probability and Examples Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha, PostNetwork Academy Partition of a Sample Space A set of events \(E_1, E_2, E_3, E_4\) represents a partition of the sample space \(S\) if: \( E_i \cap E_j = \emptyset \) for \( i \neq j \) (pairwise disjoint).
Law of Total Probability and Examples Read More »