 25.2.25.1.1: Find the maximum likelihood estimate for the parameter f.L of a nOl...
 25.2.25.1.2: Apply the maximum likelihood method to the normal distribution with...
 25.2.25.1.3: (Binomial distribution) Derive a maximum likelihood estimate for p.
 25.2.25.1.4: Extend Prob. 3 as follows. Suppose that 111 times 11 trials were ma...
 25.2.25.1.5: Suppose that in Prob. 4 we made 4 times 5 trials and A happened 2, ...
 25.2.25.1.6: Consider X = Number of independent trials IImil all el'ent A occurs...
 25.2.25.1.7: In Prob. 6 find the maximum likelihood estimate of p corresponding ...
 25.2.25.1.8: In rolling a die. suppose that we get the first Six in the 7th tria...
 25.2.25.1.9: (Poisson distribution) Apply the maximum likelihood method to the P...
 25.2.25.1.10: (Uniform distribution) Show that in the case of the parameters a an...
 25.2.25.1.11: Find the maximum likelihood estimate of e in the density f(x) = ee...
 25.2.25.1.12: In Prob. I I. find the mean f.L. substitute it in fex). find the ma...
 25.2.25.1.13: Compute e in Prob. 11 from the sanlple 1.8, 0.4. 0.8. 0.6. 1.4. Gra...
 25.2.25.1.14: Do the same task as in Frob. 13 if the given sample is 0.5.0.7.0.1....
 25.2.25.1.15: CAS EXPERIMENT. Maximum Likelihood Estimates. (MLEs). Find experime...
Solutions for Chapter 25.2: Point Estimation of Parameters
Full solutions for Advanced Engineering Mathematics  9th Edition
ISBN: 9780471488859
Solutions for Chapter 25.2: Point Estimation of Parameters
Get Full SolutionsThis textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 9. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9780471488859. Chapter 25.2: Point Estimation of Parameters includes 15 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 15 problems in chapter 25.2: Point Estimation of Parameters have been answered, more than 46198 students have viewed full stepbystep solutions from this chapter.

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!

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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

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

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

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.