Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving
4th Edition
ISBN: 9780128045251
Author: Stormy Attaway Ph.D. Boston University
Publisher: Elsevier Science
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 1, Problem 28E
To determine
To find:
The MATLAB expressions for
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A basic formula in probability is P(AUB) = P(A) + P(B) − P(ANB). (You can think
of this as a probability version of the fact that the size of a union of two sets is the sum
of their sizes minus the size of the intersection.) This is the first case of the principle of
inclusion and exclusion. Noting that P(ANB) ≥ 0 (probabilities are nonnegative) we
have P(AUB) ≤ P(A) + P(B), the probability of at least one of two events is at most
the sum of the probabilities of the two events.
The Boole-Bonferroni inequality extends this to multiple events:
P(E₁ U… U Ek) ≤ P(E1) + P(E2) + ··· + P(Ek)
or in compact notation P(U₁₁) <= P(Ei).
=1
i=1
Use mathematical induction to prove this.
2. Consider n x n matrices A, D, P, P-1 where P-1 indicates the inverse of P and D is a
diagonal matrix, the only nonzero entries are on the diagonal, d¿¿ with di; = 0 if i ‡ j.
(a) Assume that A
=
PDP and hence AP
=
PD. Explain why each column of P
is an eigenvector of A. That is, if x is the jth column of P then Ax = λ for some
number (the eigenvalue). What is \ in terms of entries of D?
(b) Prove by induction that A = PDP-¹.
Statistics question!
i need help prop
Chapter 1 Solutions
Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving
Ch. 1 - Prob. 1.1PCh. 1 - Prob. 1.2PCh. 1 - Prob. 1.3PCh. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Prob. 1ECh. 1 - Prob. 2ECh. 1 - Prob. 3ECh. 1 - Prob. 4E
Ch. 1 - Prob. 5ECh. 1 - Prob. 6ECh. 1 - Prob. 7ECh. 1 - Prob. 8ECh. 1 - Prob. 9ECh. 1 - Prob. 10ECh. 1 - Prob. 11ECh. 1 - Prob. 17ECh. 1 - Prob. 12ECh. 1 - Prob. 13ECh. 1 - Prob. 14ECh. 1 - Prob. 15ECh. 1 - Prob. 16ECh. 1 - Prob. 18ECh. 1 - Prob. 19ECh. 1 - Prob. 20ECh. 1 - Prob. 21ECh. 1 - Prob. 22ECh. 1 - Prob. 23ECh. 1 - Prob. 24ECh. 1 - Prob. 25ECh. 1 - Prob. 26ECh. 1 - Prob. 27ECh. 1 - Prob. 28ECh. 1 - Prob. 29ECh. 1 - Prob. 30ECh. 1 - Prob. 31ECh. 1 - Prob. 32ECh. 1 - Prob. 33ECh. 1 - Prob. 34ECh. 1 - Prob. 35ECh. 1 - Prob. 36E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Square matrices with entries +1 and -1 with largest determinant appear in several applications. We have not yet defined determinant but that is not relevant here. See the text Chapter 3 introductory example for an application of these matrices to an accurate weighing schemes for multiple small objects. These also are related to Reed-Muller error correcting codes used to communicate with early spacecraft sent to Mars and to Hadamard designs used in design of statistical experiments. It turns out that these matrices have entries +1 and -1 and each pair of columns orthogonal. They are called Hadamard matrices. Their size must be 2 × 2 or n x n where n is a multiple of 4. It is conjectured that they exist for all multiples of 4 but this is not solved. A 2 × 2 Hadamard matrix is H2 using blocks that are H₂ is 1 = } ] and a 4 x 4 Hadamard matrix formed 1 1 1 1 H2 H2 1 −1 1 -1 H4 = H2 -H2 -1 −1 1 From the description above and orthogonality, we formally define a Hadamard matrix of order n as…arrow_forwardFor matrix A assume that (ATA)-¹ exists. The projection matrix onto the column space of A is P = A(ATA)-¹AT. (We haven't defined column space yet but that is not needed here.) (a) Prove that P² = P. = = = (b) Prove that for all 6, Añ 6 has a solution & if and only if P₁ = 6 has a solution 7. That is show that if there exists a ū such that Pu 6 then there exists a v such that Av 6 and conversely show that if there exists a v such that Av = 6 then there exists a ū such that Pū = b. Use the given information to describe a v in terms of u and A that 'works' and for the converse describe a ū in terms of 7 and A that 'works'.arrow_forwardFor both of the following make use of the matrix multiplication definition: If A is m × n and B is n xp then (AB)ij = Σ=1(A)ik (B)kj. (a) The trace of a square matrix is the sum of its diagonal elements. Writing Tr(A) for the trace of an n × n matrix this is Tr(A) = 1 A. Prove that Tr(AB) = Tr(BA). Assume that A is m × n, then B is n × m in order for both to be defined. (b) If L and M are n×n lower triangular matrices, prove that the product LM is lower triangular. A matrix A is lower triangular if (A)ij O whenever j > i. =arrow_forward
- 17?module_item_id=4856618 was.pdx. Given = 0.1714 and n = 35 for the high income group, Test the claim that the proportion of children in the high income group that drew a picture of the nickel too large is smaller than 50%. Test at the 0.03 significance level. a. Identify the correct alternative hypothesis: Op = .50 Op.50 Oμ=.50 Op>.50 Op <.50 b. The test statistic formula set up with numbers is as follows: Provide all the decimal places. p-P x= = p-(1-p) 16 (1- ))/) The final answer for the test statistic from technology (Excel or Ti Calculator functions NOT from the above formula) is as follows: Round to 4 decimal places. x = c. Using the P-value method, the P-value is: Round to 4 decimal places. d. Based on this, we O Reject Ho O Fail to reject Ho e. Which means O There is not sufficient evidence to support the claim O There is not sufficient evidence to warrant rejection of the claim O There is sufficient evidence to warrant rejection of the claim O The sample data supports the…arrow_forwardTest the claim that the proportion of people who own cats is smaller than 20% at the 0.025 significance level. The first HELP video explains how to do a similar problem on Ti Calculator and the second HELP video shows how to use Excel Calculator for a similar problem. The null and alternative hypothesis would be: Ho p=0.2 Ho p=0.2 Ho: p=0.2 Ho p=0.2 Ho: Ha p0.2 Ha p>0.2 Ha p>0.2 Ha: p<0.2 Ha: о о о 0.2 Ho: p=0.2 <0.2 Ha: 0.2 о The test is: right-tailed two-tailed left-tailed Based on a sample of 800 people, 14% owned cats The p-value is: Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis Question Help: Video 1 Video 2 Submit Question E F3 F4 LL E ° M365 14 $ (to 2 decimals) UP T 合 D DELL Channel Deta F5 F6 F7 F8 F9 F10 P 205 % 6 & 87 * 8 RT Y Darrow_forwardWhat is the detailed solution for question and answer 7c? How to get the frequency densities of 98 and 15?arrow_forward
- I need help in this question properly . I need help in this statistics question.arrow_forwardWhat is the explanation of the solution and answer to the problem: Boxes of floor tiles are to be offered for sale at a special price of $75. The boxes claim to contain at least 100 tiles each. b. How may the seller benefit if the numbers 12,16,7,8,21,4,11,6,5 and 10 are used to draw the stem-and-leaf diagram instead of the actual numbers of tiles? Answer: Seller may notice that 10+16+7+8+21+4+11+6+5+10=100,which means that 11 (rather than ten) boxes of 100 tiles could be offered for sale.arrow_forwardWhat is the explanation of the solution and answer to the problem: Boxes of floor tiles are to be offered for sale at a special price of $75. The boxes claim to contain at least 100 tiles each. b. How may the seller benefit if the numbers 12,16,7,8,21,4,11,6,5 and 10 are used to draw the stem-and-leaf diagram instead of the actual numbers of tiles? Answer: Seller may notice that 10+16+7+8+21+4+11+6+5+10=100,which means that 11 (rather than ten) boxes of 100 tiles could be offered for sale.arrow_forward
- Table Summary: A table with 5 rows and 5 columns. The columns are titled y and the column heads are 0, 1, 2, 3, and 4. The rows are titled X and the row heads are 0, 1, 2, 3, and 4. X 0 y 1 2 3 4 0 0.03 0.01 1 0.09 0.01 0.05 0.08 0.03 0.01 0.02 0.01 2 0.09 3 0.04 0.05 0.07 0.04 0.02 0.06 0.04 0.07 0.04 0.02 0.03 0.04 0.03 0.02 Refer to Exercise 9. a. Find μx+Y. b. Find σx+Y. c. Find P(X + Y = 5).arrow_forwardAssume that the cost of an engine repair is $50, and the cost of a transmission repair is $100. Let T represent the total cost of repairs during a one-hour time interval. y X 0 1 2 3 0 0.13 0.10 0.07 0.03 1 0.12 0.16 0.08 0.04 2 0.02 0.06 0.08 0.04 3 0.01 0.02 0.02 0.02 Find uT. Find σT. Find P (T=250).arrow_forwardFor continuous random variables X and Y with joint probability density function a. Find P(X > 1 and Y > 1). xe-(x+2y) f(x, y) = x > 0 and y > 0 0 otherwise b. Find the marginal probability density functions fx(x) and fy(y). c. Are X and Y independent? Explain.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY