Central Limit Theorem: Statement, Formula, Examples
The central limit theorem says that averages of large random samples follow a normal distribution, whatever the population looks like. This guide covers the statement, standard error, conditions, and six examples.
Nov 11, 2026#Statistics
Probability A Intersection B Formula with Examples
The probability a intersection b formula is P(A ∩ B) = P(A) × P(B A), which becomes P(A)P(B) only when the events are independent. This article gives five worked examples.
Nov 7, 2026#Formula
Expected Value Formula with Worked Examples
The expected value formula is E(X) = ∑ x · P(x), each outcome multiplied by its probability and added. This article gives five worked examples.
Nov 7, 2026#Formula
Empirical Probability Formula with Examples
The empirical probability formula is P(E) = (number of times E occurred)/(total trials). This article gives five worked examples and the theoretical contrast.
Nov 7, 2026#Formula
Conditional Probability Formula with Examples
The conditional probability formula is P(B A) = (P(A ∩ B))/(P(A)), the probability of B once A is known. This article gives five worked examples.
Nov 7, 2026#Formula
Coin Toss Probability Formula with Examples
The coin toss probability formula gives any specific sequence of n fair tosses a probability of (1/2)ⁿ. This article gives five worked examples.
Nov 7, 2026#Formula
Prime Factorization Formula with Worked Examples
The prime factorization formula writes any integer above 1 as n = p₁ a₁ × p₂ a₂ × …, a product of prime powers. This article gives five worked examples.
Nov 7, 2026#Formula
Linear Interpolation Formula with Worked Examples
The linear interpolation formula is y = y₁ + ((x-x₁)(y₂-y₁))/(x₂-x₁), estimating a value between two known points. This article gives five worked examples.
Nov 7, 2026#Formula
Least Common Multiple Formula with Examples
The least common multiple formula is LCM(a,b) = (a × b)/(HCF(a,b)). This article gives the prime factorisation method, five worked examples, and the common errors.
Nov 7, 2026#Formula
Inverse Variation Formula - Definition and Examples
The inverse variation formula is y = k/x, equivalently xy = k, so one quantity falls as the other rises. This article gives five worked examples.
Nov 7, 2026#Formula
Half Life Formula with Worked Examples
The half life formula is N = N₀ (1/2) t/t 1/2, halving the quantity once per half-life. This article gives five worked examples.
Nov 7, 2026#Formula
Dividing Fractions Formula with Worked Examples
The dividing fractions formula is a/b ÷ c/d = a/b × d/c, multiplying by the reciprocal of the second fraction. This article gives five worked examples.
Nov 7, 2026#Formula
Amplitude Formula for Sine and Cosine Waves
The amplitude formula is A for y = Asin(Bx+C)+D, or equivalently (max-min)/2. This article gives five worked examples.
Nov 7, 2026#Formula
De Moivre Formula with Worked Examples
The de moivre formula states that (cosθ + isinθ)ⁿ = cos nθ + isin nθ. This article gives five worked examples including nth roots.
Nov 7, 2026#Formula
Direction of a Vector Formula with Examples
The direction of a vector formula is θ = (y/x), adjusted for the quadrant the vector lies in. This article gives five worked examples.
Nov 7, 2026#Formula
Resultant Vector Formula with Worked Examples
The resultant vector formula gives the magnitude of two combined vectors as R = √(A²+B²+2ABcosθ). This article gives five worked examples and the angle trap.
Nov 7, 2026#Formula
Maths Formula for Class 6 with Examples
Every maths formula for class 6 gathered in one place, covering perimeter, area, volume, averages, ratio and integers, with worked examples and the common errors.
Nov 7, 2026#Formula
Maths Formula for Class 8 with Examples
Every maths formula for class 8 gathered in one place, covering algebraic identities, exponent rules, mensuration and commercial arithmetic, with worked examples.
Nov 7, 2026#Formula
Maths Formula for Class 11 with Examples
Every maths formula for class 11 gathered in one place, covering sequences, trigonometry, the binomial theorem, permutations, complex numbers and conics.
Nov 7, 2026#Formula
Maths Formula for Class 12 with Examples
Every maths formula for class 12 gathered in one place, covering derivatives, integrals, vectors, three dimensional geometry and probability, with worked examples.
Nov 7, 2026#Formula