Continuous Distribution

Continuous Distribution tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩnh vực kinh...

Int. J. Med. Sci. 2009, 6 http://www.medsci.org 37IInntteerrnnaattiioonnaall JJoouurrnnaall ooff MMeeddiiccaall SScciieenncceess 2009; 6(1):37-42 © Ivyspring International Publisher. All rights reserved Research Paper Continuous Non-Invasive Arterial Pressure Technique Improves Patient Monitoring during Interventional Endoscopy Sylvia Siebig, Felix Rockmann, Karl Sabel, Ina Zuber-Jerger, Christine Dierkes, Tanja Brünnler and Christian E. Wrede Department of Internal Medicine I, University of Regensburg, Germany  Correspondence to: Sylvia Siebig, MD, Department of Internal Medicine I, University of Regensburg, D-93042 Regens-burg, Germany, Tel.: +49-941/944-7010; Fax: +49-941/944-7021; E-Mail: Sylvia.siebig@klinik.uni-r.de Received: 2008.11.17; Accepted: 2009.01.10; Published: 2009.01.20 Abstract Introduction: Close monitoring of arterial blood pressure (BP) is a central part of cardio-vascular surveillance of patients at risk for hypotension. Therefore, patients undergoing di-agnostic and therapeutic procedures with the use of sedating agents are monitored by dis-continuous non-invasive BP measurement (NIBP). Continuous non-invasive BP monitoring based on vascular unloading technique (CNAP®, CN Systems, Graz) may improve patient safety in those settings. We investigated if this new technique improved monitoring of pa-tients undergoing interventional endoscopy. Methods: 40 patients undergoing interventional endoscopy between April and December 2007 were prospectively studied with CNAP® in addition to standard monitoring (NIBP, ECG and oxygen saturation). All monitoring values were extracted from the surveillance network at one-second intervals, and clinical parameters were documented. The variance of CNAP® values were calculated for every interval between two NIBP measurements. Results: 2660 minutes of monitoring were recorded (mean 60.1±34.4 min/patient). All pa-tients were analgosedated with midazolam and pethidine, and 24/40 had propofol infusion (mean 90.9±70.3 mg). The mean arterial pressure for CNAP® was 102.4±21.2 mmHg and 106.8±24.8 mmHg for NIBP. Based on the first NIBP value in an interval between two NIBP measurements, BP values determined by CNAP® showed a maximum increase of 30.8±21.7% and a maximum decrease of 22.4±28.3% (mean of all intervals). Discussion: Conventional intermittent blood pressure monitoring of patients receiving se-dating agents failed to detect fast changes in BP. The new technique CNAP® improved the detection of rapid BP changes, and may contribute to a better patient safety for those un-dergoing interventional procedures. Key words: continuous non-invasive blood pressure, procedural sedation, endoscopy, cardiovas-cular monitoring, hypotension. Introduction Cardiovascular complications including ar-rhythmia, ischemia and hypotension during inter-ventional endoscopy, are not common, but neverthe-less higher than previously reported, and may cause harm to patients [1, 2]. In elderly patients and in those with compromised cardiovascular function even short episodes of hypotension may cause extensive prob-lems. Hence close monitoring of the arterial blood pressure (BP) is a central part of cardiovascular sur-veillance in these patients. Theoretically, this is guar-anteed at best by invasive monitoring with an in-tra-arterial catheter, but this would put patients at risk Int. J. Med. Sci. 2009, 6 http://www.medsci.org 38for adverse events like infections or necrosis. There-fore, patients undergoing diagnostic and therapeutic procedures with the use of sedating agents are moni-tored by discontinuous non-invasive BP measurement (NIBP) with measure intervals between 3 to 15 min-utes as standard. However, hypotensive Continuous Distribution Continuous Distribution By: OpenStaxCollege Continuous Distribution Class Time: Names: Student Learning Outcomes • The student will compare and contrast empirical data from a random number generator with the uniform distribution Collect the DataUse a random number generator to generate 50 values between zero and one (inclusive) List them in [link] Round the numbers to four decimal places or set the calculator MODE to four places Complete the table Calculate the following: 1/3 Continuous Distribution ¯ x = _ s = _ first quartile = _ third quartile = _ median = _ Organize the Data Construct a histogram of the empirical data Make eight bars Construct a histogram of the empirical data Make five bars Describe the Data In two to three complete sentences, describe the shape of each graph (Keep it simple Does the graph go straight across, does it have a V shape, does it have a hump in the middle or at either end, and so on One way to help you determine a shape is to draw a smooth curve roughly through the top of the bars.) Describe how changing the number of bars might change the shape Theoretical Distribution In words, X = _ The theoretical distribution of X is X ~ U(0,1) In theory, based upon the distribution X ~ U(0,1), complete the following μ = σ = first quartile = third quartile = median = 2/3 Continuous Distribution Are the empirical values (the data) in the section titled Collect the Data close to the corresponding theoretical values? Why or why not? Plot the Data Construct a box plot of the data Be sure to use a ruler to scale accurately and draw straight edges Do you notice any potential outliers? If so, which values are they? Either way, justify your answer numerically (Recall that any DATA that are less than Q1 – 1.5(IQR) or more than Q3 + 1.5(IQR) are potential outliers IQR means interquartile range.) Compare the Data For each of the following parts, use a complete sentence to comment on how the value obtained from the data compares to the theoretical value you expected from the distribution in the section titled Theoretical Distribution minimum value: _ first quartile: _ median: _ third quartile: _ maximum value: _ width of IQR: _ overall shape: _ Based on your comments in the section titled Collect the Data, how does the box plot fit or not fit what you would expect of the distribution in the section titled Theoretical Distribution? Discussion Question Suppose that the number of values generated was 500, not 50 How would that affect what you would expect the empirical data to be and the shape of its graph to look like? 3/3 APPENDICES Appendix 1: QUESTIONNAIRE The following questionnaire is conducted to investigate issues relating to the pronunciation of the first year students at the English Department, College of Foreign Languages, Vietnam National University, Hanoi. Please tick the most appropriate options according to you.Part 1: Personal Information1. What is your name?…………………………………………………2. When did you begin studying English?a. Since primary schoolb. From grade 6-9 c. From grade 10-12 d. From grade 6-123. Which English curriculum did you follow at your secondary school?a. Three-year b. Seven-year c. Pilot program (7 years)4. Did you study in an English specialized secondary school?a. Yes b. NoPart 2: Pronunciation learning at secondary schools5. How often did you listen to authentic English at your secondary school?a. No time b. < 20 mins/week c. 20- 45 mins/week d. 45-60 mins/week6. How do you judge the pronunciation of your Vietnamese teachers of English at your secondary school?a. poor b. average c. good d. excellent (native-like)7. How often were you taught English pronunciation in the class when you were at your secondary school?a. Less than 20 minutes per weekI b. From 20-45 minutes per weekc. More than 45 minutes per weekd. There was no pronunciation lesson but the teacher taught the pronunciation of new words and corrected students’ pronunciation mistakes during the lesson. (If yes, how long approximately? .)8. When you look up new words in the dictionary, what did you often do?a. looked at its meaning onlyb. looked at its pronunciation and meaning, then pronounced it in mindc. looked at its pronunciation and meaning, then pronounced it aloudPart 3: Attitude and problems with English pronunciation9. How important is pronunciation do you think?a. Not important b. Important10. What make pronunciation difficult for you?a. There are sounds and phonetic rules that do no exist in Vietnamese.b. My local dialect affects me badly.c. My phonetic ability is not good d. Nobody corrects my pronunciation for me. e. I have no one to practice speaking English with.f. Your own problem:…………………………………………………………………Thank you very much for your help!!!II Appendix 2: PRETEST (MOCK SPEAKING TEST 1)Part one: Read aloud the following passage:Another feature of many leisure activities is the introduction to a whole new social work, providing companionship with other like-minded people. New friends can be made through joining a music club, for instance. And social relationship can be strengthened through a share interest in football. The media opens up this experience to everyone who wants to participate, even if they don’t play.An essential aspect of leisure is that we can pick hobbies to suit our personality, our needs and our wallet, and we can drop them at any time. This control is crucial, as people benefit from feeling that they’re making their own decisions. That’s one reason why children need to choose their own hobbies, instead of having them imposed by their parents. (Time to waste, Objective IELTS, Intermediate, Teacher’ book, CHAPTER ONE: INTRODUCTION1.1 Rationale The trend of globalization in every field all over the world has given foreign languages in general and English in particular a greater role than ever before. As English is largely used in international settings, the ability to communicate in real-life situations is very important. Therefore, speaking plays an essential role because without it, communication cannot take place directly between people. Dealing with how to improve speaking skills, learners face the problem of pronunciation. A consideration number of learners’ pronunciation errors and how they inhibit successful communication is a good reason for the justification of why it is important to teach pronunciation to learners. There is a great number of books relating to the teaching of English pronunciation, most of which refer to specific exercises to help students achieve better pronunciation. However, in my experience as a teacher of English for three years, I have witnessed many cases in which students are able to do pronunciation exercises, but fail to have proper pronunciation in their real-life speaking. Thus, a good mark in doing pronunciation exercises in written form does not accompany good pronunciation.In my opinion, the problem lies in the fact that students do not receive adequate feedback from the teacher on their pronunciation performance. Some students even do not know how to form certain sounds in English. Therefore, it is impossible for them to have genuine production of sounds and sentences. Despite this, little can be done about this due to a vast number of factors, the most serious of which is the high student-teacher ratio in Vietnamese universities, which is about 25 to one (at universities in which English is a major). The teachers hardly have enough time to pay attention and give correction to every student’ speaking performance in general and pronunciation in particular. As a result, students are unable to identify their weak aspects. All of these motivated me to conduct an action research on the use of continuous feedback with the aim at improving the first year students’ English pronunciation.1 1.2 Statement of the problemAs a teacher at the English Department, College of Foreign Languages, Hanoi National University, I have realized the fact that the first-year students have a lot of problems concerning their pronunciation. It is true that they speak English in all English classes (twelve periods a week) and teachers are alert to help them with their pronunciation problems. However, after a year of learning, their pronunciation doesn’t seem to improve much, not to mention the fact that their frequent mistakes are maintained as the first day they enter the university. This reflects the fact that the present teaching and learning of English pronunciation is not very effective. As O’Connor (2002) stated, “clear, concise feedback matched to standards will promote student achievement”, feedback plays a very important role in the teaching of any foreign language skill because without it, students would have a vague picture of what they are really weak at and Probability in Computing © 2010, Quoc Le & Van Nguyen Probability for Computing 1 LECTURE 7: CONTINUOUS DISTRIBUTIONS AND POISSON PROCESS Agenda Continuous random variables.  Uniform distribution  Exponential distribution © 2010, Quoc Le & Van Nguyen Probability for Computing 2 Poisson process Queuing theory Continuous Random Variables Consider a roulette wheel which has circumference 1. We spin the wheel, and when it stops, the outcome is the clockwise distance X from the “0” mark to the arrow. Sample space Ω consists of all real numbers in [0, 1). Assume that any point on the circumference is equally likely to © 2010, Quoc Le & Van Nguyen Probability for Computing 3 Assume that any point on the circumference is equally likely to face the arrow when the wheel stops. What’s the probability of a given outcome x? Note: In an infinite sample space there maybe possible events that have probability = 0. Recall that the distribution function F(x) = Pr(X ≤ x). and f(x) = F’(x) then f(x) is called the density function of F(x). Continuous Random Variables f(x)dx = probability of the infinitesimal interval [x, x + dx). Pr(a ≤X<b) =  b dx x f ) ( © 2010, Quoc Le & Van Nguyen Probability for Computing 4 Pr(a ≤X<b) = E[X] = E[g(X)] =  a dx x f ) (    dxxfxg )()(    dxxxf )( Joint Distributions Def: The joint distribution function of X and Y is F(x,y) = Pr(X ≤ x, Y ≤ y). = where f is the joint density function. f(x, y) =     y x dudvvuf ),( ),( 2 yxF yx   © 2010, Quoc Le & Van Nguyen Probability for Computing 5 Marginal distribution functions F X (x)=Pr(X ≤x) and F Y (y)=Pr(Y ≤y). Example: F(x,y) = 1- e -ax – e -by + e -(ax+by) , x, y >= 0.  F X (x)=F(x,∞) = 1-e -ax .  F Y (y)=1-e -by .  Since F X (x)F Y (y) = F(x, y)  X and Y are independent. Conditional Probability What is Pr(X≤3|Y=4)? – Both numerator and denominator = 0. Rewriting Pr(X≤3|Y=4)? = ) 4 4 | 3 Pr( lim      Y X © 2010, Quoc Le & Van Nguyen Probability for Computing 6 Rewriting Pr(X≤3|Y=4)? = Pr(X≤x|Y=y) = ) 4 4 | 3 Pr( lim 0        Y X   x u Y du yf yuf )( ),( Uniform Distribution Used to model random variables that tend to occur “evenly” over a range of values Probability of any interval of values proportional to its width Used to generate (simulate) random variables from virtually any distribution © 2010, Quoc Le & Van Nguyen Probability for Computing 7 Used to generate (simulate) random variables from virtually any distribution Used as “non-informative prior” in many Bayesian analyses           elsewhere 0 1 )( bya ab yf            by bya ab ay ay yF 1 0 )( Uniform Distribution - expectation   )(3 ))(( )(33 11 2)(2 ))(( )(22 11 )( 2 2 22333 22 222 ab abbaab ab aby ab dy ab yYE ab ab abab ab aby ab dy ab yYE b a b a b a b a                                                    © 2010, Quoc Le & Van Nguyen Probability for Computing 8     )(2887.0 12 12 )( 12 )( 12 2 12 )2(3)(4 23 )( )()( 3 )( 2 2222222 2 22 2 2 2 2 ab abab ababbaabababba ababba YEYEYV abba                           Additional Properties Lemma 1: Let X be a uniform random variable on [a, b]. Then, for c ≤ d, Pr(X ≤c|X ≤d)= (c-a)/(d- a). That is, conditioned on the fact that X ≤d, X is uniform on [a, d]. © 2010, Quoc Le & Van Nguyen Probability for Computing 9 uniform on [a, d]. Lemma 2: Let X 1 , X 2 , …, X n be independent uniform random variables over [0, 1], Let Y 1 , Y 2 , …, Y n be the same values as X 1 , X 2 , …, X n in increasing sorted order. Then E[Y k ] = k/(n+1). Exponential Distribution Right-Skewed distribution with maximum at y =0 Random variable can only take on positive values Used to model inter-arrival times/distances for a Poisson process © 2010, Quoc Le & Van Nguyen Probability for Computing 10 Poisson process [...]... Van Nguyen Probability for Computing 14 ... might change the shape Theoretical Distribution In words, X = _ The theoretical distribution of X is X ~ U(0,1) In theory, based upon the distribution X ~ U(0,1), complete the.. .Continuous Distribution ¯ x = _ s = _ first quartile = _ third quartile = _ median = _... the following μ = σ = first quartile = third quartile = median = 2/3 Continuous Distribution Are the empirical values (the data) in the section titled Collect the Data close