Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer.You can borrowideas from gpt, but please do not believe its answer.Very very grateful! Given a set X ‡ Ø and p = X consider the collection of subsets ofTp = {U ≤X | p & U}U{X}.(i) Show that Tp is a topology on X. It is called the excluded point topology.(ii) Describe the closure {p} and the interior {p}° of the singleton set {p} with respectto the excluded point topology.(iii) Decide whether or not (X, Tp) is first countable and justify your answer.Exercise 1.X given byIn Lemma 2.15 we saw how taking the closure of a set interacts with the basic relationsand operations from set-theory (inclusions, unions, intersections). We can obviously ask thesame question about the operation of taking the interior of a set.

We have to show that τp is a topology on X, we need to verify three properties:1. Both the empty set…

Exercise 1. X given by Given a set X 0 and p = X consider the collection of subsets of Tp = {UCX|p&U}U{X}. (i) Show that Tp is a topology on X. It is called the excluded point topology. (ii) Describe the closure {p} and the interior {p} of the singleton set {p} with respect to the excluded point topology. (iii) Decide whether or not (X, Tp) is first countable and justify your answer.

Exercise 1. X given by Given a set X 0 and p = X consider the collection of subsets of Tp = {UCX|p&U}U{X}. (i) Show that Tp is a topology on X. It is called the excluded point topology. (ii) Describe the closure {p} and the interior {p} of the singleton set {p} with respect to the excluded point topology. (iii) Decide whether or not (X, Tp) is first countable and justify your answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A man is on trial accused of murder in the first degree. The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent. This situation can be modeled as a hypothesis test with the following hypotheses: Ho : The defendant is innocent. Ho: The defendant is guilty. Practice Activity https://mylabs.px.pearsoned.com/Pegasus/Modules/AssessmentTool/Presentation/frm intAssetID=4000002448047076&mode%3DclientFeedback&AssetLinklD=400000038336E nLinkID=0&from3sp&DRTID=0&CreateModulelD=0&madd%3D&IsModule=&dsid%3&Vi Explain the meaning of a Type I error. O Concluding that the defendant is guilty when in fact he is innocent O Failing to reject the hypothesis that the defendant is innocent when in fact he is guilty Concluding that the defendant is guilty when in fact he is guilty Failing to reject the hypothesis that the defendant is innocent when in fact he is innocent
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Bb Take Test: OStax-Q6 - 22F M10 X Bb Take Test: OStax-Q3 - 22F M10 X C bbhosted.cuny.edu/webapps/assessment/take/take.jsp?course_assessment_id=_2344863_1&course_id=_2186498_1&content_id=_70984604_1&question_... Docs Bb Welcome, Diana -... ments-22F M104pq [3 X Moving to another question will save this response. Question 2 The graph of a function f(x) is given. Answer the question. f(x) -5-4- -2 -2 -3 +4- +5+ e. Domain (f) ✓ Image(f) ✓ f(-1) 2 If f(x) = 9, then x = ? x Untitled document question will save this response a. (-4,5) b.4 c. 0 d. (-∞, ∞ ) e. [-2,4] f. [-5, 4] g. [-2, 4.1] h. Undefined Q
Can you help me with the code for this in R please? 2. The article ["CSI Effect Has Juries Wanting More Evidence" (USA Today, 2004)](https://usatoday30.usatoday.com/news/nation/2004-08-05-csi-effect_x.htm) examines how the popularity of crime-scene investigation television shows in influencing jurors' expectation of what evidence should be produced at a trial. In a survey of 500 potential jurors, one study found that 350 were regular watchers of at least one crime-scene forensics television series. i) Assuming that it is reasonable to regard this sample of 500 potential jurors as representative of potential jurors in the US, use the given information to construct and interpret a 95\% confidence interval for the proportion of all potential jurors who regularly watch at least one crime-scene investigation series. ii) Using the same sample proportion as part (i), construct a 95\% confidence interval for same proportion but instead use a sample size of 50. iii)…
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