 24.7.24.1.113: Four fair coins are tossed simultaneously. Find the probability fun...
 24.7.24.1.114: If the probability of hitting a target in a single shot is 10% and ...
 24.7.24.1.115: In Prob. 2, if the probability of hitting would be 5% and we fired ...
 24.7.24.1.116: Suppose that 3% of bolts made by a machine are defective, the defec...
 24.7.24.1.117: Let X be the number of cars per minute passing a certain point of s...
 24.7.24.1.118: Suppose thar a telephone switchboard of some company on the average...
 24.7.24.1.119: (RutherfordGeiger experiments) In 1910. E. Rutherford and H. Geige...
 24.7.24.1.120: A process of manufacturing screws is checked every hour by inspecti...
 24.7.24.1.121: Suppose that in the production of 50n resistors, nondefective item...
 24.7.24.1.122: Let P = lo/c be the probability that a certain type of lightbulb wi...
 24.7.24.1.123: Guess how much less the probability in Prob. 10 would be if the sig...
 24.7.24.1.124: Suppose that a certain type of magnetic tape contains. on the averd...
 24.7.24.1.125: Suppose thar a test for extrasensory perception consists of naming ...
 24.7.24.1.126: A carton contains 20 fuses, 5 of which are defective. Find the prob...
 24.7.24.1.127: (Multinomial distribution) Suppose a trial can result in precisely ...
 24.7.24.1.128: TEAM PROJECT. Moment Generating Function. The moment generating fun...
Solutions for Chapter 24.7: Binomial. Poisson, and Hypergeometric Distributions
Full solutions for Advanced Engineering Mathematics  9th Edition
ISBN: 9780471488859
Solutions for Chapter 24.7: Binomial. Poisson, and Hypergeometric Distributions
Get Full SolutionsChapter 24.7: Binomial. Poisson, and Hypergeometric Distributions includes 16 full stepbystep solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 9. Since 16 problems in chapter 24.7: Binomial. Poisson, and Hypergeometric Distributions have been answered, more than 46198 students have viewed full stepbystep solutions from this chapter. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9780471488859. This expansive textbook survival guide covers the following chapters and their solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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.)

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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).

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·

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