MYLAB MATH WITH PEARSON ETEXT FOR MATHEM
6th Edition
ISBN: 9780136470137
Author: Pirnot
Publisher: PEARSON
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Textbook Question
Chapter 1.CR, Problem 13CR
Follow the instructions for this “trick” starting with several different numbers of your choice. Make a conjecture as to what result you get in each case. Use algebra and deductive reasoning to explain why your conjecture is correct.
| a. | Choose any natural number. |
| b. | Multiply the number by 8. |
| c. | Add 12 to the product you just found. |
| d. | Divide the results of part (c) by 4. |
| e. | Subtract 3. |
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Students have asked these similar questions
4. Prove that, for any random variable X, the minimum of EIX-al is attained for
a = med (X).
8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined
as a product of independent, identically distributed random variables with mean
1 (under the so-called null hypothesis), and the, sometimes more convenient,
log-likelihood, log L, which was a sum of independent, identically distributed
random variables, which, however, do not have mean log 1 = 0.
(a) Verify that the last claim is correct, by proving the more general statement,
namely that, if Y is a non-negative random variable with finite mean, then
E(log Y) log(EY).
(b) Prove that, in fact, there is strict inequality:
E(log Y) < log(EY),
unless Y is degenerate.
(c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a
glimpse on (b).
2. Derive the component transformation equations for tensors shown be-
low where [C] = [BA] is the direction cosine matrix from frame A to
B.
B[T] = [C]^[T][C]T
3. The transport theorem for vectors shows that the time derivative can
be constructed from two parts: the first is an explicit frame-dependent
change of the vector whereas the second is an active rotational change
of the vector. The same holds true for tensors. Starting from the
previous result, derive a version of transport theorem for tensors.
[C] (^[T])[C] =
dt
d
B
dt
B
[T] + [WB/A]B[T] – TWB/A]
(10 pt)
(7pt)
Chapter 1 Solutions
MYLAB MATH WITH PEARSON ETEXT FOR MATHEM
Ch. 1.1 - In Exercise 1-4, draw a picture to illustrate each...Ch. 1.1 - In Exercises 1-4, draw a picture to illustrate...Ch. 1.1 - In Exercise 1-4, draw a picture to illustrate each...Ch. 1.1 - In Exercises 1-4, draw a picture to illustrate...Ch. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10E
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