MATHEMATICS
Resources & Insights
Explore mathematics, the foundational science of numbers, patterns, and logical reasoning. Learn key topics including algebra, geometry, calculus, statistics, and number theory. Ideal for students, educators, and enthusiasts seeking to develop problem-solving skills and apply mathematical concepts in science, technology, finance, and everyday life.
λ (lambda) in Poisson distribution
In probability theory and statistics, λ (lambda) is a parameter used to represent the average rate or average number of events occurring in a fixed interval in the context of a Poisson distribution. READ MORE...
Derive the Second Moment of the Poisson Distribution
Derive the formula of Variance of the Poisson Distribution READ MORE...
Suppose the diameter of aerosol particles in a particular application is uniformly distributed between 2 and 6 nanometers. Find the probability that a randomly measured particle has diameter greater than 3 nanometers.
uniformly distributed aerosol particles between 2 and 6 nanometers READ MORE...
Mastering Probability Theory: A Comprehensive Guide to Random Variable
Probability theory is a fascinating subject that has many applications in the real world. Understanding the basics of random variables and probability distributions is essential for anyone working in a field that deals with uncertainty. By mastering probability theory, you can make better decisions and improve your ability to analyze and interpret data. READ MORE...
Practical Examples of Continuous Random Variables
Practical illustrations of Random Variables that we are exposed to in our daily life READ MORE...
Trigonometric Functions
The six trigonometric functions are defined below. Refer to the above diagram to get the relational picture. sinθ = \( \dfrac {\mathrm{perpendicular}} {\mathrm{hypotenuse}} = \dfrac {p}{h} \) cosθ = \( \dfrac {\mathrm{base}} {\mathrm{hypotenuse}} = \dfrac {b}{h} \) tanθ = \( \dfrac {\mathrm{perpendicular}} {\mathrm{base}} = \dfrac {p}{b} \) cosecθ = \( \dfrac {\mathrm{hypotenuse}} {\mathrm{perpendicular}} = \dfrac {h}{p} \) secθ = \( \dfrac {\mathrm{hypotenuse}} {\mathrm{base}} = \dfrac {h}{b} \) cotθ = \( \dfrac {\mathrm{base}} {\mathrm{perpendicular}} = \dfrac {b}{p} \) READ MORE...