 12.11.12.1.638: A distribution that shows the probabilities associated with each sp...
 12.11.12.1.639: In a probability distribution, the sum of all the probabilities mus...
 12.11.12.1.640: In the binomial probability formula, p represents the probability of .
 12.11.12.1.641: In the binomial probability formula, q represents the probability of .
 12.11.12.1.642: In Exercises 510, assume that each of the n trials is independent a...
 12.11.12.1.643: In Exercises 510, assume that each of the n trials is independent a...
 12.11.12.1.644: In Exercises 510, assume that each of the n trials is independent a...
 12.11.12.1.645: In Exercises 510, assume that each of the n trials is independent a...
 12.11.12.1.646: In Exercises 510, assume that each of the n trials is independent a...
 12.11.12.1.647: In Exercises 510, assume that each of the n trials is independent a...
 12.11.12.1.648: A Dozen Eggs An egg distributor determines that the probability tha...
 12.11.12.1.649: Facebook According to Social Media Today, as of April 2010, 41.6% o...
 12.11.12.1.650: Auto Insurance An insurance company reported that 60% of all automo...
 12.11.12.1.651: Leaving a Tip Thomas Zellner works as a waiter at Outback Steakhous...
 12.11.12.1.652: Staying Connected According to a survey conducted by American Expre...
 12.11.12.1.653: Bank Loans Records from a specific bank show that 70% of car loan a...
 12.11.12.1.654: Dolphin Drug Care When treated with the antibiotic resonocyllin, 92...
 12.11.12.1.655: Manufacturing Lightbulbs A quality control engineer at a GE lightbu...
 12.11.12.1.656: Water Heaters The probability that a specific brand of water heater...
 12.11.12.1.657: TV Purchases At a Circuit City store, 1 4 of those purchasing color...
 12.11.12.1.658: MultipleChoice Quiz Edward Dunn has to take a fivequestion multipl...
 12.11.12.1.659: Transportation to Work In a random sample of 80 working mothers in ...
 12.11.12.1.660: Selecting 6 Cards Six cards are selected from a standard deck of pl...
 12.11.12.1.661: Office Visit The probability that a person visiting Dr. Guillermo S...
 12.11.12.1.662: Aruba The island of Aruba is well known for its beaches and predict...
Solutions for Chapter 12.11: Probability
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 12.11: Probability
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 12.11: Probability includes 25 full stepbystep solutions. Since 25 problems in chapter 12.11: Probability have been answered, more than 74916 students have viewed full stepbystep solutions from this chapter. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.