0000002291 00000 n State whether this is binomial or not and state why. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. It seems very cookbookish and it frustrates me that don't have any deeper intuition for the rule. 0000102827 00000 n Why is this the case? Before the school year began, 327 rising 9th graders were selected at random to participate in a study; 109 of those students were randomly assigned to enroll in the Propel program and the remaining students served as a control group. endstream endobj 49 0 obj <>stream If we are interested in the number of students who do their homework on time, then how do we define \(X\)? Hb```f``Ma`c`Ied@ AV(0c#/)/z| .w( Xo*\;Ez.nTe7M&%~63dVWNgHuHgM>~AlcO};XG2ogk&~b``Rq ']: d \(X\) takes on the values 0, 1, 2, , 20 where \(n = 20, p = 0.41\), and \(q = 1 0.41 = 0.59\). the approximate probability that more than 10% of the 2. When estimating normality of a sampling distribution do you use the SAMPLE PROPORTION (p=0.10) or POPULATION PROPORTION (p=0.15)? The letter \(n\) denotes the number of trials. 5 16 01445 . In that case, the normal distribution is no more a good approximation of the binomial distribution, and we use the binomial distribution instead. upper bound, upper bound of one, you would say that the number of parents that use cloth diapers. 0000006086 00000 n 37 0 obj <> endobj A. Please help me here. Ask for copies of RFPs and, if possible, interview the writer(s). Occasionally, students leave their USB drive in a computer. This is going to be approximately A fair coin is flipped 15 times. The mean, \(\mu\), and variance, \(\sigma^{2}\), for the binomial probability distribution are, The standard deviation, \(\sigma\), is then. \(p + q = 1\). Use your calculator to find the probability that DeAndre scored with 60 of these shots. to be approximately normal. The proportions of participants who support each presidential candidate. _F>`i:i"G}4DUvC0%O.aVX; oEwN:CyI?^Z.][rJB$0ZZ$ 04 Q^dow9sls0m5Z/Of'-=(Gy_Zmm :Nxue&9bk rtx'XJX.COGuKtZwISOEa+9pisK Especially, when the question has an identical answer only 2 hours before you posted this. At th, Posted 3 years ago. 1/10. Available online at. So I'm going to take the question collections. Now what is our mean well {]{ H..fY!=L$Yco n"- The mean is the avarage of all numbers in a set. So the mean of our sampling So this right over here ABC College has a student advisory committee made up of ten staff members and six students. Let \(X =\) the number of pages that feature signature artists. Then find the probability that a student selected at random from the class has passed in only one subject . Subsequently, they find that Three types of customers arrive at a service station. same thing as our population proportion 0.15 and we So it's going to give me A random sample of 300 students is selected from a large group of students who use a computer-equipped classroom on a regular basis. 0000001889 00000 n \(X \sim B(n, p)\) means that the discrete random variable \(X\) has a binomial probability distribution with \(n\) trials and probability of success \(p\). Twenty questions will be loaded at random each time you attempt this review activity. Four juniors and five seniors are boys. The letter \(p\) denotes the probability of a success on one trial and \(q\) denotes the probability of a failure on one trial. pending construction projects. A binomial experiment takes place when the number of successes is counted in one or more Bernoulli Trials. Maybe using the Central Limit Theorem or something? Find the probability that DeAndre scored with more than 50 of these shots. What is all individuals, objects, or measurements whose properties are being studied? the probability that more than three pages feature signature artists. !5+K8 In a statistics class of 50 students, what is the probability that at least 40 will do their homework on time? In a high school graduating class of 300, 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year. Posted 5 years ago. A student randomly selects 10 paperback books at a store. distribution of our sample proportions is approximately f. The Cold Spring High School student government polled randomly selected seniors and asked them how much money they spent on gas in the last week. right over here of, so this is the mean, of our sampling To ensure customer satisfaction, every 35th phone call received by customer service will be monitored. You are interested in the number that believes that same sex-couples should have the right to legal marital status. Give two reasons why this is a binomial problem. Then, \(q = 0.4\). is what is the approximate probability that more than 0000002096 00000 n 4/1/2020 Day 6 Classifying Quadrilaterals. The number of trials is \(n = 20\). A random sample of 200 graduating high school seniors was polled across a particular area, it was found that 85 had taken the SAT. my distribution menu right over there and then I'm going The margin of error for this estimation is 4%. Interpret the confidence interval. There is a 95% chance that randomly selected teenagers will be part of the 60% who use Mybook as their primary social network site. However, the trials are not independent because the outcome of the first trial affects the outcome of the second trial. \(X \sim B(20, 0.41)\), Find \(P(x \leq 12)\). This is a binomial problem because there is only a success or a __________, there are a fixed number of trials, and the probability of a success is 0.70 for each trial. She records the number of siblings for each of 200 randomly selected students in the school. the true proportion for our population is 0.15, what is Acidity of alcohols and basicity of amines. Eight of the pages feature signature artists. View Test Prep - Unit_3_Test_Answer_Sheet from MATH 3 at Clovis North High. The first name drawn determines the chairperson and the second name the recorder. Elliot likes to find garden snakes in his backyard and record their lengths. by the issuing agency in the proposal. endstream endobj startxref Forty-eight percent of schools in the state offer fruit in their lunches every day. Regard the first \(50\) students in the data set as a random sample drawn from the population of part (a) and use it to test the hypothesis that the population mean exceeds \(1,510 . 3 + 5 + 6 + 7 + 13 + 17 + 35 = 86. so we could say that 10% would be right over here, At ABC College, the withdrawal rate from an elementary physics course is 30% for any given term. a`l 3 In a survey, 86 high school students were randomly selected and asked how many hours of television they had watched in the previous week. Instead, you could select more schools, get a list of all Grade 11 students from these selected schools and select a random sample of Grade 11 students from each school. For this problem: After you are in 2nd DISTR, arrow down to binomcdf. Using the sample data, the researcher estimated that 23% of the students in the population saw a movie at least once per month. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 7 14 346 (6) 15 147799 . There are 7 numbers in this set. Standard Deviation \(= \sqrt{npq} = \sqrt{80(0.613)(0.387)} \approx 4.3564\), \(P(x > 50) = 1 P(x \leq 50) = 1 \text{binomcdf}(80, 0.613, 50) = 1 0.6282 = 0.3718\), Access to electricity (% of population), The World Bank, 2013. Since this rule was invented by statisticians, it can't really be "proved." Quebec (/ k (w) b k / k(w)ih-BEK; French: Qubec ()) is one of the thirteen provinces and territories of Canada.It is the largest province by area and the second-largest by population.Much of the population lives in urban areas along the St. Lawrence River, between the most populous city, Montreal, and the provincial capital, Quebec City.Quebec is the home of the Qubcois nation. HSn$1~uGEJw+6Hy?Mw07>]u7G_WQ7nPw(2d'@TH4t[si o$;N5 https://www.thoughtco.com/standard-normal-distribution-table-3126264, Creative Commons Attribution/Non-Commercial/Share-Alike. The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). 0000003955 00000 n A is the answer. Join Manhattan Prep instructor Jamie Nelson and mbaMission as she explain the key differences among the exams and how business schools view each testand help you determine which one may be best for you. 1) 157 229 3) 157 384 2) 157 312 4) 157 456 3 A survey about television-viewing preferences was given to randomly selected freshmen and seniors at Fairport High School. Are there tables of wastage rates for different fruit and veg? In Example 5, a cluster sample would choose 100 schools and then interview every Grade 11 student from those schools. specific "yes" or "no" responses to the survey. 0.1062. HJ1Fy4/D@,x"(3#f'=d{_a3ssLgwrH8m!bOt6zdxT9k@3-d>nT.q yxd7k/1jmoq]^uwmwgfqn\&U\9[Roa7US{lQWW? Direct link to cd024's post Hi, is there a proof of t, Posted 5 years ago. The mean of \(X\) can be calculated using the formula \(\mu = np\), and the standard deviation is given by the formula \(\sigma = \sqrt{npq}\). The result is \(P(x \leq 12) = 0.9738\). Why does Mister Mxyzptlk need to have a weakness in the comics? A summary of the year-end grade point averages (GPA) for the 327 9th-grade students who were chosen for the study is shown in the table below. Enter right over here, and then Enter, there we have Select all of the statements that are true. What values does the random variable \(X\) take on? %%EOF the mean number of siblings for all students in the school. Failure is defined as a student who does not complete his or her homework on time. Official Answer and Stats are available only to registered users. It has been stated that about 41% of adult workers have a high school diploma but do not pursue any further education. No payment info required. Thus, there were 140/2 = 70 juniors and 140 - 70 = 70 seniors. extreme levels of stress during the past month, so _____ The president and vice president of the class for next year will be two of my friends, Shawn and (she, her). $65/125 = 13/25$. Of the students enrolled in the Propel program, the ratio of boys to girls is approximately 2:3. The syntax for the instructions are as follows: To calculate (\(x = \text{value}): \text{binompdf}(n, p, \text{number}\)) if "number" is left out, the result is the binomial probability table. here are 6000 people who attended a political debate at a convention center. stress during the past month. \[\sigma = \sqrt{(20)(0.41)(0.59)} = 2.20.\]. You want to find the probability of rolling a one more than three times. Here are the scores of 16 randomly selected statistics students on a test on Unit 3 and on the Here are the scores of 16 randomly selected statistics students on a test on Unit 3 and on the final exam. The Philippines (/ f l p i n z / (); Filipino: Pilipinas), officially the Republic of the Philippines (Filipino: Republika ng Pilipinas), is an archipelagic country in Southeast Asia.It is situated in the western Pacific Ocean and consists of around 7,641 islands that are broadly categorized under three main geographical divisions from north to south: Luzon, Visayas, and Mindanao. How many adult workers do you expect to have a high school diploma but do not pursue any further education? There are three candidates who are participating in the debate - Mr. Smith, Mr. Jones, or Ms. Roberts. Each game you play is independent. Click the card to flip . This page titled 4.4: Binomial Distribution is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. B. vegan) just to try it, does this inconvenience the caterers and staff? What are the key statistics about pancreatic cancer? American Cancer Society, 2013. endstream endobj 50 0 obj <>stream the 75 randomly selected students. D) It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%. But if we know the true proportion to calculate np, we are already know the true proportion why to take samples at all? Sal was doing the 160*0.15 calculation. The equivalent ACT score is found by using the formula from the first 2 parts of this question using 1.545 as the z score. Is it more likely that five or six people will develop pancreatic cancer? 0000006471 00000 n should tell the graders what you're actually typing Anna wants to estimate the mean number of siblings for each student in her school. HT= ++`2u&*}{j[Xq2* dYF!gs;U!. Which of the following is the best estimate of the number of girls enrolled in the program? There are only two possible outcomes, called "success" and, "failure" for each trial. Thus, the mean is higher than the median and answer is A. Or the Health Department might issue RFPs endstream endobj 45 0 obj <>stream Most of the entries in the NAME column of the output from lsof +D /tmp do not begin with /tmp. Read this as "\(X\) is a random variable with a binomial distribution." This may result in a somewhat larger sample than using a simple random sampling method, but it saves . Quantity A is 12.3. 0000003688 00000 n \(P(x \leq 12) = 0.9738\). If the sample of 16 adult females was chosen. endstream endobj 38 0 obj <> endobj 39 0 obj <> endobj 40 0 obj <>stream He asks a randomly selected group of 200 parents whether or not they use cloth diapers. Yes you are right. 1/4 were freshman. A) Selecting one of the 50 stores at random and then surveying each employee at that store, B) Selecting 10 employees from each store at random and then surveying each employee selected, C) Surveying the 25 highest-paid employees and the 25 lowest-paid employees, D) Creating a website on which employees can express their opinions and then using the first 50 responses. Construct a 95% confidence interval for the population standard deviation, . What is the sample? Step 1: Determine the hypotheses. if they have experienced extreme levels of stress Now, the corrected z value is z = ( x - )/ = (605 - 500)/100 = 105/100 = +1.05. greater than or equal to ten. Can someone please help with the question above? Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. distribution, so this is going to be equal to the and if it is, then we can use its mean and the standard 1190. and the standard deviation was. Connect and share knowledge within a single location that is structured and easy to search. ? L!(u3t{=2(W9f{BcPFc,aW'2 !H=VC! 0000009917 00000 n A high school newspaper doesn't This implies that 52% do not. If a student scores 1407 on the SAT, we need to find the standardized score (z score) for 1407. z = (X-)/ = (1407-1101)/198 = 1.545. This is a paper/pencil copy of a onlin thology enhancd iterin A high school randomly selected 75 of the 200 seniors at the school to take a sample college entrance exam. 0000095336 00000 n Legal. +n)i7mt`&myq3@5g3;a"AZpt:P_Um|(3>_ }AQ# k"/ The names are not replaced once they are drawn (one person cannot be two captains). She asked each of the 75 students, How many minutes per day do you typically spend reading? . in in your normal CDF function, but if we click 18) A random sample of 30 high school students is selected. A statistical experiment can be classified as a binomial experiment if the following conditions are met: There are a fixed number of trials, \(n\). rev2023.3.3.43278. In words, define the random variable \(X\). Well we'll just make this one 75. Let's see this is going to also know that our standard deviation here is going to 0000010582 00000 n Pryor, John H., Linda DeAngelo, Laura Palucki Blake, Sylvia Hurtado, Serge Tran. The standard deviation is \(\sigma = \sqrt{npq}\). State the probability question mathematically. Estimate the sample mean. endstream endobj 42 0 obj <>stream If a success is guessing correctly, then a failure is guessing incorrectly. What is the standard deviation Direct link to Shishir Iyer's post Since this rule was inven, Posted 2 years ago. endstream endobj 43 0 obj <>stream The two population proportions are equal to each other. 0000128447 00000 n hb```f``rb`a``cd@ A+s,vlq]A>'8::$i @2x``D20D00*21fbex0. x733 g9f. View Unit 3 Multiple Choice Sample Questions from ECON 105 at Sacred Heart Academy. Many Northerners _ _grate to Florida in the winter. Use a 0.05 level of significance. What legacy do we want to leave for the next 20 years? Direct link to 8091467's post where did the 8 come from, Posted 2 years ago. mean and standard deviation in order to approximate the 0.1, what is my upper bound? bell curve for a normal distribution, so something like this. The director tested the hypotheses H_0:p=0.08H0 :p=0.08 versus H_a:p . Estimate the true portion of high school graduates in this region who; The student body of a large university consists of 40% female students. - [Instructor] We're told let me click Enter there. There are lots of these on the web. and then out of our choices it would be this one right over here. Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. hTn0E|,[ubC[)>{HX,=$Q:3kXa'}t~ $A/+UUp8/wxA?>(/hP`XXjC:{28;+#T[[?vGV-y$)IDH=&*Km,8Xgm.H2N79^aHlHADb! w;Ut*["b]3'sGNM.&O C The random variable \(X =\) the number of successes obtained in the \(n\) independent trials. Students who passed only in statistics = 55-30=25 Douglas wants to estimate the percentage of homeowners that own at least one dog. %e0%rtfCB !b8I cZ,RF\i*H~XKQWX6May]uO'*B3QD5UfyfuNW)9b*k^2Kdk((00%"aC>~9_X`dp;/MSIJ{E[F`zu. c"4?Ul]dN=7Of\W 6iz?(FD2xa-7[/xOl%. This is not binomial because the names are not replaced, which means the probability changes for each time a name is drawn. 47 0 obj << /Linearized 1 /O 49 /H [ 1380 509 ] /L 249678 /E 128857 /N 8 /T 248620 >> endobj xref 47 47 0000000016 00000 n @ *\YC'YgnqmDd'a;9-(]E~Di- jJi$A Lt:R1#PNUSK>TQGNqGptoF3z;C">fGs8MSJrZ\G(k]nh]\ b1U4%]G+KvT@#7DZz>@4i4*q>EcS){E|ai1]yz'zzvnL Dw3X]bvh5ZXc,;S)8vD&Ho/2N\V2>AO?Wk&C$Z@KRFHZM}RC+1Jv|fV#X1S, 4eX~z/i"\^n=h!RE ||/weqBX` A?,/EKI1 D+Vhk/oC stratified 12. The best answers are voted up and rise to the top, Not the answer you're looking for? Each flip is independent. You want to see if the captains all play the same position. It's just that they chose 10 because if the number of successes and failures was less than that, a normal distribution became exceedingly unlikely. Go into 2nd DISTR. Think of trials as repetitions of an experiment. Among $33$ students in a class 17 of them earned A's on the midterm, $14$ earned A's on the final exam, $11$ of them did not earn $A$ on either exam. To save chart as picture, move your mouse over the graph, until a small camera icon appear. 0000006266 00000 n sample would report that they experienced extreme levels of Available online at, Newport, Frank. This would be a two-stage sampling design. 160, the true population proportion is 0.15 and that Of students selected for the survey, 1/4 were freshmen and 1/3 were sophomores. Let \(X\) = the number of workers who have a high school diploma but do not pursue any further education. endstream endobj 47 0 obj <>stream HT1)cli%c'vTYc .>qR'yI| hVmoH+1 }H$4)&E1d[6;3v y6bY2Lz`x$qQLH2VdBgA995bLYS{y`H#d( BNsZW$),OV(`$Ed02]\) [&y2-Cl / je>j2vY^OXZh|:_evyY= nMMh]W &3H:M&C'm.rL *PQ.&]N' The following example illustrates a problem that is not binomial. The hypotheses are: H 0: p = 0.80; H a: p > 0.80; where p is the proportion of college students ages 18 to 23 who have health . The California Consumer Privacy Act (CCPA) gives California residents the right to opt- out of the sale of their personal information. >[p5saNvu,3pRM_H{8y%yTU yUm`!(mN"w jiCfJUyL(u}_cuM?]lO~9u#NcqSdS1 ./c\uj=ui{=w7.BtwP?BgnEo/on;Te]l3G}cf m If 336 students were selected for the survey, how many were seniors? Is there a single-word adjective for "having exceptionally strong moral principles"? 0000001380 00000 n Why do small African island nations perform better than African continental nations, considering democracy and human development? Systematic Sample. Multistage Sample. This means that for every true-false statistics question Joe answers, his probability of success (\(p = 0.6\)) and his probability of failure (\(q = 0.4\)) remain the same. During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. The histogram below displays their answers. It appears that you are browsing the Prep Club for GRE forum unregistered! If you want to find \(P(x > 12)\), use \(1 - \text{binomcdf}(20,0.41,12)\). can answer this on your own. Thus, the chance of obtaining a sample with less than 15% seniors is about 3.6%--not very likely. Of the 300 students questioned, 180 said that they write their name on their USB drive. What is the probability that the chairperson and recorder are both students? 0 checks out and then if I take our sample size times one She randomly selected 75 names from the city phone directory and conducted a phone survey. a normal distribution so you could draw your classic An easy trick to solve it is to notice that this distribution has a long right hand tail, meaning that there are individuals with high values of hours spent on TV (higher mean) but they are few (the median is low). Direct link to Kaitlyn Anderson's post How we would solve this i, Posted 4 years ago. Direct link to pankaj3856's post How can i calculate the p, Posted 5 years ago. The two-way table gives summarizes information about seniors and juniors at a high school and the way they typically get to school. we already know that's 0.15. As a sampler all I have is sampling data, not true proportions. Because the \(n\) trials are independent, the outcome of one trial does not help in predicting the outcome of another trial. To estimate the mean salary of professors at her university, Patricia collects data by recording . The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Let n(M) = 70 ( students passed in mathematics) ; n(S) = 55 ( students passed in Statistics) ; n(M $\cap S) = 30.$, Therefore, probability of students passed in mathematics = $\frac{70}{125}; $, Probability of students passed in statistics = = $\frac{55}{125}; $, Using $$P(M \cup S) = P(M) + P(S) - P(M \cap S)$$, $$\Rightarrow P(M \cup S) = \frac{70}{125} + \frac{55}{125} - \frac{30}{125} = \frac{19}{25}$$, But the answer is wrong ; book answer is : $\frac{13}{25}$. Example 6.9. None of the above. Direct link to Parthiban Rajendran's post But if we know the true p, Posted 5 years ago. Use the TI-83+ or TI-84 calculator to find the answer. You want to find out which candidate is most popular amongst the people attending. If P (AB)=0.08 and P (B|A)=0.25, what is the probability that the selected student will be a student athlete? Qunaity A is greater than quantity B. Construct the probability distribution function (PDF). of our sampling distribution of our sample proportions is than 0.10 just like that. There are 15 math classes in 11th grade. for system administration and to provide you a personalized ad experience. sampling distribution of our sample proportions and first And our standard deviation There are only two possible outcomes called success and failure for each trial. Its contradicting. H A Which of the following sampling methods is most appropriate to estimate the proportion of all employees of the company who are satisfied with their job? The two population proportions are both 0. b. approximately normal, is it approximately normal Nick wants to estimate the percentage of homeowners that own at least one dog. We could instead take a bunch of SRSs, find each p-hat, then take the mean of all these individual sample proportions; this would make it. Given the frequency table, what is the mean? A market researcher randomly selects 200 drivers under 35 years of age and 100 drivers over 35 . Matthew wants to estimate the mean height of students attending his college. Direct link to Yao's post What is the difference th, Posted 5 years ago. Fv R8k)eDqtEY)'U.VI46U_B!YT0>6vb[+aw:mHl,.%hg(Np_`bi2@T]~fh_{bgG\+?wC|RjNI#kRS2BT%' Now the probability of selecting a student that drives to school. 0000005149 00000 n 40 randomly selected undergraduate psychology-degree program students, B. !H2+n'xF Find the mode of the following number of computers available to students at randomly selected high school libraries. Suppose that the mean of the sampling distribution for the difference in two sample proportions is 0. The standard deviation of \(X\) is \(\sigma = \sqrt{npq}\). k-gX0Yy-TVA`I 3 j5j7Y@[K$k[GVsM6hMFrK-yXW8O|}owht($|SlrOsu^,r5L'-"^vy>v]`*HrMownJ4j ZFWZg:cy''Q0X~3>#Em6 + px1K_ g/GG?E} 0 z (Single Intervals), Given the frequency table, what is the estimated mean? standard deviation of our sampling distribution? 0000011466 00000 n needs to be greater than or equal to ten and so let's So how is np threshold a valid approach? the mean number of siblings for the randomly selected students. The probability that at most 12 workers have a high school diploma but do not pursue any further education is 0.9738. this area right over here. Of students selected for the survey, 1/4 were freshmen and 1/3 were sophomores. Systematic. Direct link to Gowthamraush06's post while calculating standar. 10% of the sample replied "yes" to the question. Each student is asked how many hours he or she spent on the Internet during the previous week. 1. Using the formulas, calculate the (i) mean and (ii) standard deviation. you'll need a calculator for that, unless you're good at finding square roots with a pencil and paper. Note: these settings will only apply to the browser and device you are currently using. 1 11 . 0000009105 00000 n Data reported in this paper are drawn from The American College Testing Program (ACT) files of student records collected over the five year period from 1970-71 to 1974-75 through administration of the ACT Assessment Program. Thank you for using the timer! Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey about potential changes to next years schedule. A lacrosse team is selecting a captain. If you were taking this on 1/3 were sophomores. Administrators at Riverview High School surveyed a random sample of 100 of their seniors to see how seniors at the school felt about the lunch offering at the school's cafeteria. { "4.01:_Prelude_to_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.02:_Probability_Distribution_Function_(PDF)_for_a_Discrete_Random_Variable" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.03:_Mean_or_Expected_Value_and_Standard_Deviation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.04:_Binomial_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.05:_Geometric_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.06:_Hypergeometric_Distribution" : 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