Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Probability | Statistics & Logic 🔹 Introduction Conditional probability tells us how likely an event is, given that another event has already occurred. It’s one of the most powerful tools in probability — and one of the most misunderstood. Conditional probability connects what […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Probability & Statistics 🔹 Introduction In probability, every random event carries uncertainty — but we can still measure what happens on average. That’s what expected value (or expectation) tells us. Expected Value = the “center of gravity” of a random variable’s distribution. Similarly, […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Algebra | Functions & Graph Analysis 🔹 Why This Matters Every function tells a story — but to understand it fully, we must know: Together, these three concepts give the complete picture of any function’s behavior — algebraically and geometrically. 🧭 1️⃣ Domain […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Statistics | Probability & Data Analysis 🔹 Introduction You’ve seen the normal distribution — the classic bell curve representing continuous random variables.You’ve used it to find probabilities given Z-scores. But what if you know the probability and need to find the Z-score or […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Algebra | Functions & Graphs 🔹 What Is a Function? A function is a rule that assigns to every input (x-value) exactly one output (y-value).In notation: y=f(x)y = f(x)y=f(x) The graph of a function is the set of all points (x,y)(x, y)(x,y) that […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Statistics | Probability & Data Analysis 🔹 Introduction In statistics, most real-world measurements — like test scores, heights, or manufacturing errors — follow a bell-shaped pattern.That pattern is known as the Normal Distribution. The normal distribution is the backbone of statistical inference — […]

Mathematics is more than just numbers—it is the language of logic, problem-solving, and STEM excellence. For ambitious students in Singapore, excelling in math opens doors to top local and international universities, scholarships, and competitive STEM programs. As an IIT Guwahati and Indian Statistical Institute alumnus, published author, and passionate educator with 6+ years of global […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor & Author)Published: October 2025Category: Education | IB Mathematics | Global STEM Preparation 🔹 Introduction The International Baccalaureate (IB) is more than a qualification — it’s a framework for thinking globally and reasoning deeply. At Math By Rishabh, we are redefining IB Mathematics learning by offering […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Statistics | Probability & Inference 🔹 Introduction In real-world statistics, we often estimate population parameters using sample data. But what if the population standard deviation (σ) is unknown — which is almost always the case? That’s where the Student’s t-distribution comes in. The […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Algebra | Graphs & Functions 🔹 What Are Function Transformations? A transformation of a function changes its shape, position, or orientation on a graph — without altering its fundamental nature. Every transformation can be understood as a modification of the base function f(x)f(x)f(x). […]