CHSE Odisha Business Mathematics & Statistics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Union cardinality

For two finite sets A and B, n(A∪B) = n(A) + n(B) − n(A∩B).

Equivalence relation

A relation that is reflexive, symmetric, and transitive simultaneously.

Bijective function

A function that is both injective (one-one) and surjective (onto), so an inverse exists.

Matrix inverse condition

A square matrix A has an inverse if and only if det(A) ≠ 0; then A⁻¹ = adj(A)/det(A).

Determinant product rule

For square matrices A and B of the same order, det(AB) = det(A)·det(B).

Cramer's rule

Solves AX=B by x_i = det(A_i)/det(A), where A_i replaces column i with B, provided det(A)≠0.

Combination formula

C(n,r) = n!/[r!(n−r)!], giving the number of r-element subsets from n distinct objects.

Circular permutation

The number of arrangements of n distinct objects around a circle is (n−1)!.

AP nth term

For an arithmetic progression with first term a and common difference d, a_n = a + (n−1)d.

GP infinite sum

For a geometric progression with |r|<1, the sum to infinity is a/(1−r).

Slope of a line

For points (x1,y1) and (x2,y2), slope m = (y2−y1)/(x2−x1), provided x2≠x1.

Perpendicular lines condition

Two lines with slopes m1 and m2 are perpendicular if and only if m1·m2 = −1.

Chain rule

If y = f(u) and u = g(x), then dy/dx = (dy/du)·(du/dx).

Second derivative test

At a stationary point, f″(x)>0 gives a local minimum; f″(x)<0 gives a local maximum.

Integration by parts

∫u dv = uv − ∫v du; choose u by the ILATE order (Inverse, Logarithmic, Algebraic, Trigonometric, Exponential).

Area under a curve

The area bounded by y=f(x), the x-axis, and lines x=a and x=b is ∫_a^b |f(x)| dx.

Grouped median formula

Median = L + [(n/2 − cf)/f]·h, where L is lower class limit, cf cumulative frequency before median class, f its frequency, h class width.

Coefficient of variation

CV = (standard deviation / mean) × 100%; a smaller CV indicates greater consistency.

Pearson correlation coefficient

r = [nΣxy − ΣxΣy] / √{[nΣx²−(Σx)²][nΣy²−(Σy)²]}; it lies between −1 and 1.

Regression line of y on x

y − ȳ = b_yx(x − x̄), where b_yx = r·σ_y/σ_x is the regression coefficient of y on x.

Conditional probability

P(A|B) = P(A∩B)/P(B), the probability of A given that B has occurred, with P(B)>0.

Binomial mean and variance

For X ~ B(n,p), mean = np and variance = npq, where q = 1−p.

Poisson distribution

P(X=r) = e^(−λ)λ^r/r!; both mean and variance equal λ.

Fisher's ideal index

P_F = √(P_L × P_P), the geometric mean of Laspeyres and Paasche indices; it satisfies time and factor reversal tests.

Laspeyres price index

P_L = (Σp1q0 / Σp0q0) × 100, using base-year quantities q0 as weights.

Time reversal test

An index number formula satisfies it if P01 × P10 = 1, where P10 is the index computed in reverse time order.

Power set cardinality

If a set A has n elements, its power set P(A) has 2^n elements.

Skew-symmetric matrix

A square matrix A satisfying A′ = −A; all diagonal entries are zero.

Permutation with repetition

The number of arrangements of n objects where p, q, r are identical is n!/(p!q!r!).

AM–GM inequality

For positive numbers, arithmetic mean ≥ geometric mean, with equality only when all numbers are equal.

Distance from point to line

For line Ax+By+C=0 and point (x1,y1), distance = |Ax1+By1+C| / √(A²+B²).

Marginal revenue

The derivative of total revenue with respect to quantity: MR = dR/dx; profit is maximised where MR = MC.