 11.8.1: In 12, the numbers that each pointer can land on and their respecti...
 11.8.2: In 12, the numbers that each pointer can land on and their respecti...
 11.8.3: The tables in 34 show claims and their probabilities for an insuran...
 11.8.4: The tables in 34 show claims and their probabilities for an insuran...
 11.8.5: An architect is considering bidding for the design of a new museum....
 11.8.6: A construction company is planning to bid on a building contract. T...
 11.8.7: It is estimated that there are 27 deaths for every 10 million peopl...
 11.8.8: A 25yearold can purchase a oneyear life insurance policy for $10...
 11.8.9: 910 are related to the SAT, described in Check Point 4 on page 752 ...
 11.8.10: 910 are related to the SAT, described in Check Point 4 on page 752 ...
 11.8.11: A store specializing in mountain bikes is to open in one of two mal...
 11.8.12: An oil company is considering two sites on which to drill, describe...
 11.8.13: In a product liability case, a company can settle out of court for ...
 11.8.14: A service that repairs air conditioners sells maintenance agreement...
 11.8.15: 1519 involve computing expected values in games of chance. A game i...
 11.8.16: 1519 involve computing expected values in games of chance. A game i...
 11.8.17: 1519 involve computing expected values in games of chance. Another ...
 11.8.18: 1519 involve computing expected values in games of chance. The spin...
 11.8.19: 1519 involve computing expected values in games of chance. For many...
 11.8.20: What does the expected value for the outcome of the roll of a fair ...
 11.8.21: Explain how to find the expected value for the number of girls for ...
 11.8.22: How do insurance companies use expected value to determine what to ...
 11.8.23: Describe a situation in which a business can use expected value.
 11.8.24: If the expected value of a game is negative, what does this mean? A...
 11.8.25: The expected value for purchasing a ticket in a raffle is  +0.75. ...
 11.8.26: Make Sense? In 2629, determine whether each statement makes sense o...
 11.8.27: Make Sense? In 2629, determine whether each statement makes sense o...
 11.8.28: Make Sense? In 2629, determine whether each statement makes sense o...
 11.8.29: Make Sense? In 2629, determine whether each statement makes sense o...
 11.8.30: A popular state lottery is the 5/35 lottery, played in Arizona, Con...
 11.8.31: Refer to the probabilities of dying at any given age in the table p...
 11.8.32: This activity is a group research project intended for people inter...
Solutions for Chapter 11.8: Expected Value
Full solutions for Thinking Mathematically  6th Edition
ISBN: 9780321867322
Solutions for Chapter 11.8: Expected Value
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 32 problems in chapter 11.8: Expected Value have been answered, more than 61043 students have viewed full stepbystep solutions from this chapter. Chapter 11.8: Expected Value includes 32 full stepbystep solutions. Thinking Mathematically was written by and is associated to the ISBN: 9780321867322. This textbook survival guide was created for the textbook: Thinking Mathematically, edition: 6.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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!

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.)

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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.

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).

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.