finite math exam 3 defs. and formulas

mean & variance, normal curves, system of linear equations

Mean

• μ = x1+x2+…+xn/n

• μ = np

Variance

• s² = (x1-E(x))²xf1+…+(xr-E(x))²xfr/n-1

• σ² = E(x²)-[E(x)]²

• σ² = npq

Standard Deviation

• s = √(x1-E(x))²xf1+…+(xr-E(x))²xfr/n-1

• σ = √npq

Binomial Random Variable

• C(n,k)(p)^k(q)^n-k

Chebyshev’s Inequality

• Pr(μ-c<=X<=μ+c)>=σ²/c²

Standard Normal Curve

• continuous probability distribution for a real valued random variable where μ = 0, σ = 1, π = 3.1416, e = 2.7183

Properties of a Normal Curve

• centered at μ, symmetric about μ, total area under the curve = 1

Conversion Formula

• z = x-μ/σ

Percentile

• a value on a scale of 100 that indicates percent of a distribution that is equal to or below it

Binomial Adjustment

• Pr(x=k) > Pr(k-0.5<=x<=k+0.5)

• Pr(x<=k) = Pr(x<=k+0.5)

• Pr(x>=k) = Pr(x>=k-0.5)

• Pr(l<=x<=m) > Pr(l-0.5<=x<=m+0.5)

Reduced Row Echelon Form

1. first non-zero number in every row is “1” called leading “pivotal”

2. leading 1 in every row is to the right of leading 1 in row above

3. If there is a row entirely of “0’s,” it must be on the bottom

4. All other entries in column with leading one must be zero

Row Operations

1. Ri<>Rj

2. Ri=aRi

3. Ri=Ri+aRj

Size of Matrix

Dimension: (# of rows) x (# of columns) > mxn

Row Matrix/Vector

Has dimension 1 x n

Column Matrix/Vector

Has dimension m x 1

Square Matrix

Has dimension nxn

Zero Matrix

All entries are zero

Identity Matrix

Denoted by In, is the matrix with 1’s down the diagonal and 0’s everywhere else