probability - Probability
5 question 2021/8/17 HW1 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw1.html 1/2 Intro to Probability - Homework Assignment 1 Please solve the problems and type the solutions up using LateX and the template provided. Naming instructions for the file you will submit are contained in the file itself. Please justify your answers and dont simply give the answer. Problem 1 How many plate numbers can be created in California format DLLLDDD, where D stands for digit and L stands for letter? What if no repetitions are allowed in the digits? Problem 2 A zip code consists of 5 digits. If the first cannot be the digit 0, how many zip codes can be generated? Problem 3 How many letter arrangements can be made from the letters of the word Iowa? How about from the letters of Connecticut? Problem 4 How many 5-card poker hands are there? (A regular deck has 52 cards). Problem 5 Assuming that you can only move to the right or down, in how many ways can you get from the top left point to the bottom right one along the depicted grid? Problem 6 If you need to split a class of 32 students in 8 groups of 4, in how many ways can you do it? Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/FnameLnameHWn.tex https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW1 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw1.html 2/2 Problem 7 If a student is required to solve 8 out of 10 assigned problems, how many choices does she have? What if the first 4 problems are mandatory? Problem 8 How many actual digit numbers exist? What if no two consecutive digits can be the same? How many numbers with at most digits exist? Numbers are to be understood as actuall numbers: 1 is a one digit number but 001 is not an actual number and certainly not a 3 digit number. Problem 9 A total of 6 people need to be selected from a set of 10 twins of different families (20 people total). How many choices are there, if it is not allowed to select two siblings? Problem 10 A total of 8 representatives need to be chosen from a group of 40 students, of which 24 are female and 16 are male. In how many ways can this be done? What if we require that there be at least 3 female and 3 male representatives? n n Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW4 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw4.html 1/3 Intro to Probability - Homework Assignment 4 Please solve the problems and type the solutions up using LateX and the template provided. Naming instructions for the file you will submit are contained in the file itself. Please justify your answers and dont simply give the answer. Problem 1 If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is for ? Problem 2 Consider an urn containing 12 balls, of which 8 are white. A sample of size 4 is to be drawn with replacement (without replacement). What is the conditional probability (in each case) that the first and third balls drawn will be white given that the sample drawn contains exactly 3 white balls? Problem 3 Three cards are randomly selected, without replacement, from an ordinary deck of 52 playing cards. Compute the conditional probability that the first card selected is a spade given that the second and third cards are spades. Problem 4 In a certain community, 36\% of the families own a dog and 22\% of the families that own a dog also own a cat. In addition, 30\% of the families own a cat. What is a. the probability that a randomly selected family owns both a dog and a cat? b. the conditional probability that a randomly selected family owns a dog given that it owns a cat? Problem 5 Urn A contains 2 white and 4 red balls, whereas urn B contains 1 white and 1 red ball. A ball is randomly chosen from urn A and put into urn B, and a ball is then randomly selected from urn B. What is a. the probability that the ball selected from urn B is white? b. the conditional probability that the transferred ball was white given that a white ball is selected from urn B? i i = 1, … , 12 Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/FnameLnameHWn.tex https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW4 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw4.html 2/3 Problem 6 a. A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random; when he flips it, it shows heads. What is the probability that it is the fair coin? b. Suppose that he flips the same coin a second time and, again, it shows heads. Now what is the probability that it is the fair coin? c. Suppose that he flips the same coin a third time and it shows tails. Now what is the probability that it is the fair coin? Problem 7 Let . Express the following probabilities as simply as possible Problem 8 A ball is in anyone of boxes and is in the -th box with probability . If the ball is in box , a search of that box will uncover it with probability . Show that the conditional probability that the ball is in box , given that a search of box did not uncover it, is Problem 9 An event is said to carry negative information about an event iff This is denoted by . Either give a proof or provide a counterexample for the following assertions a. If , then . b. If and , then . c. If and , then . Problem 10 The probability of getting a head on a single toss of a coin is . Suppose that A starts and continues to flip the coin until a tail shows up, at which point B starts flipping. Then B continues to flip until a tail comes up, at which point A takes over, and so on. Let E ⊂ F P (E|F ), P (E|F c), P (F |E), P (F |E c). n i Pi i αi j i ,  if j ≠ i,  and  ,  if i = j. Pj 1 − αiPi (1 − αi)Pi 1 − αiPi E P (E|F ) ≤ P (E). F ↘ E F ↘ E E ↘ F F ↘ E E ↘ G F ↘ G F ↘ E G ↘ E F ∩ G ↘ G p Pn,m Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW4 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw4.html 3/3 denote the probability that A accumulates a total of heads before B accumulates . Show that n m Pn,m = p Pn−1,m + (1 − p)(1 − Pm,n). Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW2 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw2.html 1/3 Intro to Probability - Homework Assignment 2 Please solve the problems and type the solutions up using LateX and the template provided. Naming instructions for the file you will submit are contained in the file itself. Please justify your answers and dont simply give the answer. Problem 1 An urn contains 3 balls: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 ball from the urn, replacing it in the box, and drawing a second ball. Describe the sample space of this experiment and for the experiment obtained not replacing the first ball in the urn. Problem 2 In an experiment, a die is rolled continually until a 5 appears, at which point the experiment stops. What is the sample space of this experiment? Let denote the event that rolls are necessary to conclude the experiment. What outcomes are contained in ? What does the event represent? Problem 3 Two dice are rolled. Using that is the event that the sum of the dice is odd, the event that at least one of the dice lands on 1, and the event that the sum is 5, describe the events , , , , and . Problem 4 A hospital administrator codes incoming patients suffering from heart disease according to whether they have insurance (code 1 if they do and 0 if they do not) and based on their condition, which can be rated as good G, fair F, or serious S. Consider an experiment that consists of producing codes for such a patient. a. Give the sample space of this experiment. b. Let be the event that the patient is in serious condition and list all outcomes in . c. Let be the event that the patient is uninsured and list all outcomes in . d. List the outcomes in . Problem 5 En n En (⋃ ∞ n=1 En) c O O1 S5 O ∩ O1 O ∪ O1 O1 ∩ S5 O ∩ O c 1 O ∩ O1 ∩ S5 S S U U S c ∪ U Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/FnameLnameHWn.tex https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW2 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw2.html 2/3 Suppose that two events , are such that and satisfy and . What are the probabilities that a. either or occurs? b. occurs but does not? c. both and occur? What happens if you dont assume that ? Problem 6 At a summer camp three activities are offered: tennis, swimming, and archery. The courses are open to the 120 summer camp participants. There are 31, 24, and 17 in these activities, respectively. There are 4 participants in all activities, 11 in tennis and swimming, 9 in tennis and archery, 7 in swimming and archery. a. If a participant is chosen at random, what is the probability that he or she is taking part exactly one activity? b. If a participant is chosen at random, what is the probability that he or she is taking part in no activity? c. If two participants are chosen at random, what is the probability that they are both taking part in exactly one activity? Problem 7 Consider three fair dice with the following digits on their faces. The blue die has 2 faces each with 1, 5, and 9 on them. The red die shows the digits 3, 4, and 8 twice each and the green one 2,6, 7 twice each. Two players choose a die each and then roll it. The winner is the player who rolls the highest number. If you had the opportunity to choose whether to pick your die first, would you do it or rather go second? Problem 8 Let E, F, and G be three events. Use them to describe the following events: a. Of the three only occurs. b. Both E and G occur , but F does not. c. At least one event occurs of the three. d. At least two of the events occur. e. None of the events occur. f. All occur. E F E ∩ F = ∅ P (E) = 0.3 P (F ) = 0.5 E F E F E F E ∩ F = ∅ F Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW2 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw2.html 3/3 g. Exactly two events occur. h. At most three of the events occur. i. At most one of them occurs. Problem 9 If and , show that . In general, prove Bonferronis inequality, i.e., that Problem 10 An urn contains yellow and black balls. They are withdrawn one at a time until a total of yellow ones one are obtained. Find the probability that this happens on drawing number for any . P (E) = 0.9 P (F ) = 0.8 P (E ∩ F ) ≥ 0.7 P (E ∩ F ) ≥ P (E) + P (F ) − 1 n m y ≤ n k k ≤ m + n Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW3 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw3.html 1/3 Intro to Probability - Homework Assignment 3 Please solve the problems and type the solutions up using LateX and the template provided. Naming instructions for the file you will submit are contained in the file itself. Please justify your answers and dont simply give the answer. Problem 1 If 8 identical computers are to be divided among 4 lab rooms, how many divisions are possible? How many if each room must receive at least 1 computer? Problem 2 Suppose that 10 fish are caught in a pond that contains 5 distinct types of fish. a. How many different outcomes are possible, where an outcome consists in the number of fish caught of each of the 5 types? b. How many outcomes are possible if 3 of the 10 fish caught are trout? c. How many when at least 2 of the 10 are trout? Problem 3 Prove that by connecting the formula to a concrete situation (i.e. interpreting its meaning). Show that the formula implies Problem 4 Consider a tournament of contestants in which the outcome is an ordering of these contestants, with ties allowed. That is, the outcome partitions the players into groups, with the first group consisting of the players that tied for first place, the next group being those that tied for the next-best position, and so on. Let denote the number of different possible outcomes. For instance, , since, in a tournament with 2 contestants, player 1 could be uniquely first, player 2 could be uniquely first, or they ( ) = ( )( ) + ( )( ) + ⋯ + ( )( ) n + m r n 0 m r n 1 m r − 1 n r m 0 ( ) = ( ) 2 + ( ) 2 + ⋯ + ( ) 2 . 2n n n 0 n 1 n n n N (n) N (2) = 3 Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/FnameLnameHWn.tex https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW3 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw3.html 2/3 could tie for first. a. List all possible outcomes when . b. Setting , show that without resorting to any computation. c. Find for . Problem 5 In how many ways can identical balls be placed into urns so that the th urn contains at least balls, for each ? Assume that . Problem 6 A, B, and C take turns flipping a coin in that order.The first one to get a head wins. Explain why the sample space of this experiment can be defined by by describing what it means. Then use it to describe the following events: Problem 7 A retail establishment accepts either the American Express or the VISA credit card. A total of 24\% of its customers carry an American Express card, 61\% carry a VISA card, and 11\% carry both cards. What percentage of its customers carry a credit card that the establishment will accept? Problem 8 Two cards are randomly selected from an ordinary playing deck (52 cards). What is the probability that one of the cards is an ace and the other one is either a ten, a jack, a queen, or a king? This combinations is called a black jack. Problem 9 Prove that n = 3 N (0) = 1 N (n) = n ∑ i=1 ( )N (n − i) = n−1 ∑ i=0 ( )N (i), n i n i N (n) n = 3, 4 n r i mi i = 1, … , r n ≥ ∑ r i=1 mi 1, 01, 001, 0001, 00001, … WA = ‘‘A wins , WB = ‘‘B wins ,  and (WA ∪ WB) c. P (E ∩ F c ) = P (E) − P (E ∩ F ). Home About Video Lectures Short Videos Problem Sets FAQ Resources Contact https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/courseIndex.html https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.about.html 2021/8/17 HW3 - Intro to Probability https://www.math.uci.edu/~gpatrick/homeDepot/130aOnline/.hw3.html 3/3 Problem 10 Consider an experiment whose sample space consists of a countably infinite number of points. Show that not all points can be equally likely. Can all points have a positive probability of occurring? 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Your assignment may be more than 5 paragraphs but not less. INSTRUCTIONS:  To access the FNU Online Library for journals and articles you can go the FNU library link here:  https://www.fnu.edu/library/ In order to n that draws upon the theoretical reading to explain and contextualize the design choices. Be sure to directly quote or paraphrase the reading ce to the vaccine. Your campaign must educate and inform the audience on the benefits but also create for safe and open dialogue. A key metric of your campaign will be the direct increase in numbers.  Key outcomes: The approach that you take must be clear Mechanical Engineering Organic chemistry Geometry nment Topic You will need to pick one topic for your project (5 pts) Literature search You will need to perform a literature search for your topic Geophysics you been involved with a company doing a redesign of business processes Communication on Customer Relations. Discuss how two-way communication on social media channels impacts businesses both positively and negatively. Provide any personal examples from your experience od pressure and hypertension via a community-wide intervention that targets the problem across the lifespan (i.e. includes all ages). Develop a community-wide intervention to reduce elevated blood pressure and hypertension in the State of Alabama that in in body of the report Conclusions References (8 References Minimum) *** Words count = 2000 words. *** In-Text Citations and References using Harvard style. *** In Task section I’ve chose (Economic issues in overseas contracting)" Electromagnetism w or quality improvement; it was just all part of good nursing care.  The goal for quality improvement is to monitor patient outcomes using statistics for comparison to standards of care for different diseases e a 1 to 2 slide Microsoft PowerPoint presentation on the different models of case management.  Include speaker notes... .....Describe three different models of case management. visual representations of information. They can include numbers SSAY ame workbook for all 3 milestones. You do not need to download a new copy for Milestones 2 or 3. When you submit Milestone 3 pages): Provide a description of an existing intervention in Canada making the appropriate buying decisions in an ethical and professional manner. Topic: Purchasing and Technology You read about blockchain ledger technology. Now do some additional research out on the Internet and share your URL with the rest of the class be aware of which features their competitors are opting to include so the product development teams can design similar or enhanced features to attract more of the market. The more unique low (The Top Health Industry Trends to Watch in 2015) to assist you with this discussion.         https://youtu.be/fRym_jyuBc0 Next year the $2.8 trillion U.S. healthcare industry will   finally begin to look and feel more like the rest of the business wo evidence-based primary care curriculum. Throughout your nurse practitioner program Vignette Understanding Gender Fluidity Providing Inclusive Quality Care Affirming Clinical Encounters Conclusion References Nurse Practitioner Knowledge Mechanics and word limit is unit as a guide only. The assessment may be re-attempted on two further occasions (maximum three attempts in total). All assessments must be resubmitted 3 days within receiving your unsatisfactory grade. You must clearly indicate “Re-su Trigonometry Article writing Other 5. June 29 After the components sending to the manufacturing house 1. In 1972 the Furman v. Georgia case resulted in a decision that would put action into motion. Furman was originally sentenced to death because of a murder he committed in Georgia but the court debated whether or not this was a violation of his 8th amend One of the first conflicts that would need to be investigated would be whether the human service professional followed the responsibility to client ethical standard.  While developing a relationship with client it is important to clarify that if danger or Ethical behavior is a critical topic in the workplace because the impact of it can make or break a business No matter which type of health care organization With a direct sale During the pandemic Computers are being used to monitor the spread of outbreaks in different areas of the world and with this record 3. Furman v. Georgia is a U.S Supreme Court case that resolves around the Eighth Amendments ban on cruel and unsual punishment in death penalty cases. The Furman v. Georgia case was based on Furman being convicted of murder in Georgia. Furman was caught i One major ethical conflict that may arise in my investigation is the Responsibility to Client in both Standard 3 and Standard 4 of the Ethical Standards for Human Service Professionals (2015).  Making sure we do not disclose information without consent ev 4. Identify two examples of real world problems that you have observed in your personal Summary & Evaluation: Reference & 188. Academic Search Ultimate Ethics We can mention at least one example of how the violation of ethical standards can be prevented. Many organizations promote ethical self-regulation by creating moral codes to help direct their business activities *DDB is used for the first three years For example The inbound logistics for William Instrument refer to purchase components from various electronic firms. During the purchase process William need to consider the quality and price of the components. In this case 4. A U.S. Supreme Court case known as Furman v. Georgia (1972) is a landmark case that involved Eighth Amendment’s ban of unusual and cruel punishment in death penalty cases (Furman v. Georgia (1972) With covid coming into place In my opinion with Not necessarily all home buyers are the same! When you choose to work with we buy ugly houses Baltimore & nationwide USA The ability to view ourselves from an unbiased perspective allows us to critically assess our personal strengths and weaknesses. This is an important step in the process of finding the right resources for our personal learning style. Ego and pride can be · By Day 1 of this week While you must form your answers to the questions below from our assigned reading material CliftonLarsonAllen LLP (2013) 5 The family dynamic is awkward at first since the most outgoing and straight forward person in the family in Linda Urien The most important benefit of my statistical analysis would be the accuracy with which I interpret the data. The greatest obstacle From a similar but larger point of view 4 In order to get the entire family to come back for another session I would suggest coming in on a day the restaurant is not open When seeking to identify a patient’s health condition After viewing the you tube videos on prayer Your paper must be at least two pages in length (not counting the title and reference pages) The word assimilate is negative to me. I believe everyone should learn about a country that they are going to live in. It doesnt mean that they have to believe that everything in America is better than where they came from. It means that they care enough Data collection Single Subject Chris is a social worker in a geriatric case management program located in a midsize Northeastern town. She has an MSW and is part of a team of case managers that likes to continuously improve on its practice. The team is currently using an I would start off with Linda on repeating her options for the child and going over what she is feeling with each option.  I would want to find out what she is afraid of.  I would avoid asking her any “why” questions because I want her to be in the here an Summarize the advantages and disadvantages of using an Internet site as means of collecting data for psychological research (Comp 2.1) 25.0\% Summarization of the advantages and disadvantages of using an Internet site as means of collecting data for psych Identify the type of research used in a chosen study Compose a 1 Optics effect relationship becomes more difficult—as the researcher cannot enact total control of another person even in an experimental environment. Social workers serve clients in highly complex real-world environments. Clients often implement recommended inte I think knowing more about you will allow you to be able to choose the right resources Be 4 pages in length soft MB-920 dumps review and documentation and high-quality listing pdf MB-920 braindumps also recommended and approved by Microsoft experts. The practical test g One thing you will need to do in college is learn how to find and use references. References support your ideas. College-level work must be supported by research. You are expected to do that for this paper. You will research Elaborate on any potential confounds or ethical concerns while participating in the psychological study 20.0\% Elaboration on any potential confounds or ethical concerns while participating in the psychological study is missing. Elaboration on any potenti 3 The first thing I would do in the family’s first session is develop a genogram of the family to get an idea of all the individuals who play a major role in Linda’s life. After establishing where each member is in relation to the family A Health in All Policies approach Note: The requirements outlined below correspond to the grading criteria in the scoring guide. At a minimum Chen Read Connecting Communities and Complexity: A Case Study in Creating the Conditions for Transformational Change Read Reflections on Cultural Humility Read A Basic Guide to ABCD Community Organizing Use the bolded black section and sub-section titles below to organize your paper. For each section Losinski forwarded the article on a priority basis to Mary Scott Losinksi wanted details on use of the ED at CGH. He asked the administrative resident