 155 .1: The sets of data for two different statistical studies are identica...
 155 .2: Elaine said that the variance is the square of the standard deviati...
 155 .3: In 39, the given values represent data for a population. Find the v...
 155 .4: In 39, the given values represent data for a population. Find the v...
 155 .5: In 39, the given values represent data for a population. Find the v...
 155 .6: In 39, the given values represent data for a population. Find the v...
 155 .7: In 39, the given values represent data for a population. Find the v...
 155 .8: In 39, the given values represent data for a population. Find the v...
 155 .9: In 39, the given values represent data for a population. Find the v...
 155 .10: In 1016, the given values represent data for a sample. Find the var...
 155 .11: In 1016, the given values represent data for a sample. Find the var...
 155 .12: In 1016, the given values represent data for a sample. Find the var...
 155 .13: In 1016, the given values represent data for a sample. Find the var...
 155 .14: In 1016, the given values represent data for a sample. Find the var...
 155 .15: In 1016, the given values represent data for a sample. Find the var...
 155 .16: In 1016, the given values represent data for a sample. Find the var...
 155 .17: To commute to the high school in which Mr. Fedora teaches, he can t...
 155 .18: A hospital conducts a study to determine if nurses need extra staff...
 155 .19: The ages of all of the students in a science class are shown in the...
 155 .20: The table shows the number of correct answers on a test consisting ...
 155 .21: The table shows the number of robberies during a given month in 40 ...
 155 .22: Products often come with registration forms. One of the questions u...
Solutions for Chapter 155 : VARIANCE AND STANDARD DEVIATION
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 155 : VARIANCE AND STANDARD DEVIATION
Get Full SolutionsThis textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 22 problems in chapter 155 : VARIANCE AND STANDARD DEVIATION have been answered, more than 30874 students have viewed full stepbystep solutions from this chapter. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. Chapter 155 : VARIANCE AND STANDARD DEVIATION includes 22 full stepbystep solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Outer product uv T
= column times row = rank one matrix.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.