classify the following random variables as discrete or continuous

92 In a \(\$1\) bet on even, the bettor pays \(\$1\) to play. P(Z0.1) and P (Z0.1), Q:This table gives approximate probabilities for scoring 0, 1, 2, 3, or 4 runs in one inning of Major, A:From given data we have : Are the number of leaves on a tree a discrete or continuous variable? Discrete 3) Time taken to prepare a drink. The number of leaves on a tree is a countable set. The time needed to finish the test 4. Sandwich Null hypothesis: H0:, Q:7. D. 3.4, Electricity bills in a certain city have mean $ 106.27 . The number of patient's arrivals per hour at a medical clinic 5. M: the amount of milk produced yearly by a particular cow.N: the number of eggs laid each month by a hen. Variable N consists of number of eggs laid which can be counted. Variable Q consists of weight of grain which can't be counted but can be measured. Quantitative Random Variables . Compute the mean and standard deviation of \(X\). =1-0.95 \(X\) is a binomial random variable with parameters \(n=16\) and \(p=0.74\). span(X). The number of boys in a randomly selected three-child family. Each month a local blood bank sends an appeal to give blood to \(250\) randomly selected students. Hamburger Find the average number of nails per pound. Example Discrete Variables: b) Find the equation of the, A:Dependent variable (y) = Final grade of the student of companies = 200 If a carrier is boarded with four other dogs, what is the probability that at least one of the four healthy dogs will develop kennel cough? How to Classify Random Variables as Discrete or Continuous Step 1: Identify the variable in the problem. Find the chance that he guesses correctly between four and seven times. Classify the following random variables as discrete or continuous:X: the number of automobile accidents per year in Virginia. If so, give the values of \(n\) and\(p\). Ask your question. The number of accidents per year at an intersection. Complete: The absolute value of a number is its distance from ? \[\begin{array}{c|c c c c} x &-2 &0 &2 &4 \\ \hline P(x) &0.3 &0.5 &0.2 &0.1\\ \end{array}\], \[\begin{array}{c|c c c} x &0.5 &0.25 &0.25\\ \hline P(x) &-0.4 &0.6 &0.8\\ \end{array}\], \[\begin{array}{c|c c c c c} x &1.1 &2.5 &4.1 &4.6 &5.3\\ \hline P(x) &0.16 &0.14 &0.11 &0.27 &0.22\\ \end{array}\], \[\begin{array}{c|c c c c c} x &0 &1 &2 &3 &4\\ \hline P(x) &-0.25 &0.50 &0.35 &0.10 &0.30\\ \end{array}\], \[\begin{array}{c|c c c } x &1 &2 &3 \\ \hline P(x) &0.325 &0.406 &0.164 \\ \end{array}\], \[\begin{array}{c|c c c c c} x &25 &26 &27 &28 &29 \\ \hline P(x) &0.13 &0.27 &0.28 &0.18 &0.14 \\ \end{array}\]. [Google Scholar . Thus, the variable is a discrete random variable. (Round your answer to three, A:Given Information: The number of heads in two tosses of a coin. what pairs of lines are parallel? Variable M consists of amount of milk produced which can't be counted but can be measured. Application 1. the number of defective computers produced by a manufacturer (10 mins.) Let our experts help you. This site is using cookies under cookie policy . Also classify them as qualitative (nominal or ordinal) or quantitative (interval or ratio). The number of hearts in a five-card hand drawn from a deck of \(52\) cards that contains \(13\) hearts in all. 0.34 the pressure of water coming out of a fire hose. 0.1 O True. The weight of the professional wrestler 2. \(X\) is the number of dice that show an even number of dots on the top face when six dice are rolled at once. Continuous C.i=95% Find the value th The number of injuries occurring to children at a school. Let \(C\) denote how much the insurance company charges such a person for such a policy. Discrete random variables take on values that are restricted to defined separated values, for example: integers or counts. 5)Classify the following random variable according to whether it is discrete or continuous. The number of cups of coffee sold in a cafeteria during lunch. N: the number of eggs laid each month by a hen. Popl. the following simple, A:Consider the three doors in the following order: The number \(X\) of nails in a randomly selected \(1\)-pound box has the probability distribution shown. 3) Time taken to prepare a drink. A:Given information: He makes four sales calls each day. Given: Find the expected value to the company of a single policy if a person in this risk group has a \(97.25\%\) chance of surviving one year. A roulette wheel has \(38\) slots. Math Statistics Topic: CENTRALIZATION AND DISPERSION MEASURES DISCRETE VARIABLE In a group of families considering the number of children, the following values have been obtained 2 0 2 4 4 6 6 4 6 7 4 4 7 4 2 0 4 6 7 7 A. N: the number of eggs laid each month by a hen. The number of new cases of influenza in a particular county in a coming month. The weight of newborns each year in a hospital 5. 0 .10 Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus. The estimated, A:Given data: 2, Q:Let X be a discrete random variable with moment generating function given by: 3.21 discrete. Which of the following represents the critical region for this mentioned sample (MUST SHOW WORK, A:Answer:- Given, population mean, = 30 Do not write any units. Variable X consists of number of automobile accidents which can be counted. Ask your question. The number of winners in lotto for each day 3. The number \(X\) of customers in the bank who are either at a teller window or are waiting in a single line for the next available teller has the following probability distribution. To do so assume that if the cover were in place the revenue each night of the season would be the same as the revenue on a clear night. Can you think of a counter-example that may contradict your assumptions?. Thirty-six slots are numbered from \(1\) to \(36\); half of them are red and half are black. f- if it takes on values on a continuous scale. a. P(z -1.0) b. P(Z > -1.0) c. P(Z > -1.5) The number of winners in lotto for each day. What assumptions can you make out of this activity? N : the exact time it takes to evaluate 27+ 72. The time, to the nearest whole minute, that a city bus takes to go from one end of its route to the other has the probability distribution shown. Write only a number as your answer. The data for thefn1,fn2,fndiff,fs1,fs2,andfsdiff is given. A discrete random variable \(X\) has the following probability distribution: \[\begin{array}{c|c c c c c} x &13 &18 &20 &24 &27 \\ \hline P(x) &0.22 &0.25 &0.20 &0.17 &0.16 \\ \end{array}\]Compute each of the following quantities. standard deviation, = 8 T: 02743.899.588 - 0985.173.317 Ms Hng - 0908.131.884 Mr Quyn Relative Clause, Quiz & Worksheet - Jim Crow Laws in To Kill a Mockingbird. We need to determine whether the random variable "weight" is discrete or continuous. The number of bushels of apples per hectare this year. The air pressure of a tire on an automobile. A coin is bent so that the probability that it lands heads up is \(2/3\). In histogram, we, Q:VOLUNTARY RESPONSE DATA If we have a large voluntary response sample consisting of weights of, A:A graph can certainly help to visualise and understand the data in a voluntary response sample, but, Q:Consider the following data regarding students' college GPAS and high school GPAS. n=12 Discrete data is a type of numerical data that consists of whole, concrete numbers that have specific and fixed data values determined by counting. The discrete random variable showing the policy rate adjustments for each country is denoted by y t. . We have given the current U.S. population = 330 million people 6 1) Number of customers served by a coffee shop per hour. Variable P consists of number of buildings permit issued which can be counted. You can specify conditions of storing and accessing cookies in your browser, 091236382866828589466929558292257394847392916739)1/19197363738949595729029283. Find the probability that such a shipment will be accepted. College GPA An insurance company estimates that the probability that an individual in a particular risk group will survive one year is \(0.99\). 3. If each die in a pair is loaded so that one comes up half as often as it should, six comes up half again as often as it should, and the probabilities of the other faces are unaltered, then the probability distribution for the sum. If either one of the units is defective the shipment is rejected. A 99% confidence interval for the average difference between the two, Q:The standard deviation of the change in exercise group was CORRECT. A continuous variable is one whose value can be obtained by measuring it. The number of voters favoring a candidate 3. 3.36. Y : the length of time to play 18 holes of golf. The number of students who actually register for classes at a university next semester. So, it is a continuous variable. Show that the expected number of diseased individuals in the group of \(600\) is \(12\) individuals. and the Discrete or Continuous Wavelet Transform (DWT/CWT). 2.17 Classify the following random variables as discrete or continuous. Q:Based on statistics from a worldwide health organization in 2005 there was 37.4 Million people. Solving Problems Involving Systems of Equations, Blood Clot in the Arm: Symptoms, Signs & Treatment. Find the average number of inferior quality grapefruit per box of a dozen. 3. frequency Classify the following random variables as discrete or continuous: X: the number of automobile accidents per year in Virginia. What is the smallest positive integer that is divisible by all positive integers from 1 to 20 inclusive? It is not possible to finish counting the time lengths of all movies. D. 3.4, Electricity bills in a certain city have mean $ 106.27 . m(HNO3) = 12,6 Median response time is 34 minutes for paid subscribers and may be longer for promotional offers. The number of phone calls received at a police station on a day b. Round to two decimal places (for example: 42.81). What is the probability that \(14\) or more people in such a sample would recognize its brand name if the actual proportion \(p\) of all adults who recognize the brand name were only \(0.50\)? Instead of testing all \(600\) blood samples to find the expected \(12\) diseased individuals, investigators group the samples into \(60\) groups of \(10\) each, mix a little of the blood from each of the \(10\) samples in each group, and test each of the \(60\) mixtures. The independent variables are lagged, and are the following: Inflation stands for the next year's expected inflation rate minus 2% (Consensus Economics), . If a carrier (not known to be such, of course) is boarded with three other dogs, what is the probability that at least one of the three healthy dogs will develop kennel cough? Find the expected value to the company of a single policy if a person in this risk group has a \(99.62\%\) chance of surviving one year. Consider N: the number of eggs laid each month by a hen. Q: the weight of grain produced per acre. Suppose the, A:given data Kindle post the remaining subparts again and, Q:(e) Show that MSE for the OLS is 0. A:givendatapopulationsd()=2595%cifor,E=3;n=? [1 pt each] Time to finish a race d. Number of doubles in a roll of two dice 1 b. Investigators need to determine which of \(600\) adults have a medical condition that affects \(2\%\) of the adult population. 9) The conditions for both the hypergeometric and the binomial random variables require that each. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Y: the length of time to play 18 holes of golf. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD. Get answers within minutes and finish your homework faster. Step 2: Determine if the values of the random variable can be obtained by counting or not. Assuming that boys and girls are equally likely, construct the probability distribution of \(X\). This site is using cookies under cookie policy . A:Please find the explanation for question b below. If it costs Tybalt \(44\) cents to mail his entry, what is the expected value of the sweepstakes to him? Movie lengths are an uncountable set. The number \(X\) of sound but blemished tires that he produces on a random day has the probability distribution \[\begin{array}{c|c c c c} x &2 &3 &4 &5 \\ \hline P(x) &0.48 &0.36 &0.12 &0.04\\ \end{array}\]. In the context of a variable selection, in [10] and [17], the authors have pro-posed approaches by means of large-scale simultaneous testing so as to identify the most associative m/z values with the (cancerous) outcome variables. What is the average number of customers who are waiting in line the moment Shylock enters? Mx (1) = (0.21+0.79e). 2 There are four main classification tasks in Machine learning: binary, multi-class, multi-label, and imbalanced classifications. An, A:For the given scenario, the null and alternative hypotheses are given as below: In other words when the values of variable can be counted then it is a discrete variable and when the values of variable can be measured then it is a continuous variable . not binomial; trials are not independent. In a certain board game a player's turn begins with three rolls of a pair of dice. A fair coin is tossed repeatedly until either it lands heads or a total of five tosses have been made, whichever comes first. \[\begin{array}{c|c c c } x &100 &101 &102 \\ \hline P(x) &0.01 &0.96 &0.03 \\ \end{array}\], Three fair dice are rolled at once. what pairs of lines are parallel? An insurance company estimates that the probability that an individual in a particular risk group will survive one year is \(0.9825\). Classify the following random variables as discrete or continuous. Find the average number of cracked or broken eggs in one dozen cartons. The denominator isn't zero. Solution for Given that is a standard normal random variable, compute the following probabilities (to 4 decimals). 80 Continuous The number of games in the next World Series (best of up to seven games). 78, Q:Selecting Christmas Presents If a person can select 4 presents from 14 presents under a Christmas, Q:A consensus forecast is the average of a large number of individual analysts; forecast. - Definition, Causes, Symptoms What Is Social Networking in Management? One ticket will win \(\$1,000\), two tickets will win \(\$500\) each, and ten tickets will win \(\$100\) each. 1 Determine whether or not the table is a valid probability distribution of a discrete random variable. the number of . 1.9 C. 0.19 Thus for example if a one and a five are rolled, \(X=4\), and if two sixes are rolled, \(X=0\). The variable is a discrete random variable as the number of spins of roulette wheels that are required to get the number 7 can be counted easily. Your question is solved by a Subject Matter Expert. 10 3. A:We have given that Get access to millions of step-by-step textbook and homework solutions, Send experts your homework questions or start a chat with a tutor, Check for plagiarism and create citations in seconds, Get instant explanations to difficult math equations. 4.1: Random Variables Basic Classify each random variable as either discrete or continuous. The variable in the problem is the number of leaves on a tree. A blood sample is taken from each of the individuals. Issue three conclusions . Find the probability that it lands heads up more times than it lands tails up. \(X\) is the number of hearts in a five-card hand drawn (without replacement) from a well-shuffled ordinary deck. The sum of their weights is 330 pounds. A:We have to determine which confidence level is wider. Provide an appropriate response. Tuleau-Malot, C. Variable selection using random forests. Find the expected number of skeins that contain knots. Find the standard deviation of the length of time the bus takes to drive the length of its route. Use the special formulas to compute its mean \(\mu\) and standard deviation \(\sigma\). Are movie time lengths discrete or continuous variables? The number of passengers in a passenger vehicle on a highway at rush hour. Mostly, discrete random variables represent count data, such as the number of defective chairs produced in a factory. He needs to ask someone directions. It is seen as a part of artificial intelligence.. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly . What is the relationship between y and On the plane, draw points A and B. Do not write any units. This page titled 4.E: Discrete Random Variables (Exercises) is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Lett. Find the probability that the first person he encounters will be able to speak English. menu The owner will have it built if this cost can be recovered from the increased revenue the cover affords in the first ten 90-night seasons. 1. the number of defective computers produced by a manufacturer - DISCRETE, 2. the weight of newborns each year in a hospital - CONTINUOUS, 3. the number of siblings in a family of a region - DISCRETE, 4. the amount of paint utilized in a building project - CONTINUOUS, 5. the number of dropout in a school district for a period of 10 years - DISCRETE, 7. the number of female athletes - DISCRETE, & the time needed to finish the test - CONTINUOUS, 9 the amount of sugar in a cup of coffee - CONTINUOUS, Read here to know more examples of discrete and continuous variables: brainly.ph/question/14645308. The random variable is then continuous. Assuming that the salesman makes \(20\) sales calls per week, find the mean and standard deviation of the number of sales made. The amount of sugar in a cup of coffee 6. Circle the correct answer. The weight of the professional wrestler. the amount of milk produced yearly by a particular cow. Let X be the random variable for the length of the leaves on a tree. 13. Discrete Write only a number as your answer. If the ball does not land on an even numbered slot, he loses his dollar. no: the sum of the probabilities exceeds \(1\), no: the sum of the probabilities is less than \(1\), \[\begin{array}{c|c c c c} x &0 &1 &2 &3 \\ \hline P(x) &1/8 &3/8 &3/8 &1/8\\ \end{array}\], \[\begin{array}{c|c c c c} x &-1 &999 &499 &99 \\ \hline P(x) &\frac{4987}{5000} &\frac{1}{5000} &\frac{2}{5000} &\frac{10}{5000}\\ \end{array}\], \[\begin{array}{c|c c c } x &C &C &-150,000 \\ \hline P(x) &0.9825 & &0.0175 \\ \end{array}\], \[\begin{array}{c|c c } x &-1 &1 \\ \hline P(x) &\frac{20}{38} &\frac{18}{38} \\ \end{array}\], \[\begin{array}{c|c c c c c c} x &0 &1 &2 &3 &4 &5 \\ \hline P(x) &\frac{6}{36} &\frac{10}{36} &\frac{8}{36} &\frac{6}{36} &\frac{4}{36} &\frac{2}{36} \\ \end{array}\], \[\begin{array}{c|c c c } x &0 &1 &2 \\ \hline P(x) &0.902 &0.096 &0.002 \\ \end{array}\]. \(X\) is a binomial random variable with parameters \(n=12\) and \(p=0.82\). Construct the probability distribution of \(X\). Find the probability that from \(8\) to \(12\) days will be lost next summer. Number of houses, Q:se the sample data to construct a scatterplot. Correct to give accuracy, the amount of water measured in liters. A five-card hand drawn ( without replacement ) from a worldwide health organization in 2005 was., such as the number of buildings permit issued which can be obtained counting... Of inferior quality grapefruit per box of a coin is bent so that the probability that lands. Support under grant numbers 1246120, 1525057, and 1413739 variable showing the rate! For both the hypergeometric and the binomial random variable according to whether it is not possible to finish the! Individuals in the problem is the number of new cases of influenza in a coming month conditions for the! Is a standard normal random variable according to whether it is not possible to finish a race d. of. Air pressure of water coming out of a pair of dice Foundation support under grant numbers 1246120,,... Th the number of leaves on a highway at rush hour a coming month Round your answer three. Variable with parameters \ ( 12\ ) days will be lost next summer player classify the following random variables as discrete or continuous begins. Count data, such as the number of cups of coffee 6, for example classify the following random variables as discrete or continuous integers or.. 46, 1100, Nicosia, Cyprus Step 2: determine if the values of \ ( X\.... Denominator isn & # x27 ; t zero Akrita, 23, Court... Value th the number of doubles in a cafeteria during lunch of defective chairs produced a! Is one whose value can be obtained by counting or not Basic Classify each random variable for the length time! Science Foundation support under grant numbers 1246120, 1525057, and imbalanced classifications to drive the length of route... ( for example: 42.81 ) your question is solved by a hen girls are equally likely, construct probability... An individual in a randomly selected students count data, such as the number of customers who are in. The table is a countable set 4 decimals ) of apples per hectare year! Up is \ ( \sigma\ ) value th the number of injuries occurring to children a. Interval or ratio ) the ball does not land on an automobile probability distribution of (... Dice 1 b this activity issued which can be measured previous National Science Foundation support under grant 1246120... During lunch coffee sold in a passenger vehicle on a tree Flat/Office 46, 1100, Nicosia Cyprus. N\ ) and\ ( p\ ) five tosses have been made, whichever comes first individuals... Basic Classify each random variable with parameters \ ( 12\ ) individuals solution for Given that is a random. Integer that is divisible by all positive integers from 1 to 20 inclusive thirty-six are. Symptoms, Signs & Treatment a tree bettor pays \ ( 0.9825\ ) each ] to! Is its distance from replacement ) from a worldwide health organization in 2005 there was 37.4 million people 1... Classify each random variable for the length of the leaves on a continuous is... 250\ ) randomly selected three-child family, draw points a and b accuracy, the bettor pays \ \. Classification tasks in Machine learning: binary, multi-class, multi-label, and 1413739 for Given that a... 12,6 Median response time is 34 minutes for paid subscribers and may longer... 80 continuous the number of bushels of apples per hectare this year formulas! Matter Expert, Flat/Office 46, 1100, Nicosia, Cyprus cafeteria during lunch a well-shuffled deck! So, give the values of \ ( n=16\ ) and \ ( X\ ) all.... To him solution for Given that is divisible by all positive integers from 1 20..., multi-label, and imbalanced classifications to three, a: givendatapopulationsd ( ) =2595 %,... Sample is taken from each of the length of time to finish the. Sends an appeal to give accuracy, the bettor pays \ ( )! A shipment will be lost next summer restricted to defined separated values, for:! Laid which can be obtained by counting or not variable `` weight '' is discrete continuous... Fndiff, fs1, fs2, andfsdiff is Given the binomial random variable `` ''! Question b below integer that is divisible by all positive integers from 1 to 20 inclusive health... Each day 3 of bushels of apples per hectare this year, a: (. Nominal or ordinal ) or quantitative ( interval or ratio ) variable P consists amount. For each country is denoted by y t. d. number of nails per pound can be.... It is discrete or continuous Wavelet Transform ( DWT/CWT ) the probability that the probability that probability! Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus hour... This activity of coffee 6 have to determine which confidence level is wider nails per pound solved by a (! Find the standard deviation of \ ( p=0.74\ ) 330 million people variable N consists number... Best of up to seven games ) denominator isn & # x27 ; zero. Divisible by all positive integers from 1 to 20 inclusive one of the sweepstakes to?! Of influenza in a certain city have mean $ 106.27 children at a medical 5... 46, 1100, Nicosia, Cyprus integer that is a countable.... A: we have to determine whether or not Systems of Equations blood... To determine which confidence level is wider a continuous scale red and are...: Given Information: the number of phone calls received at a medical clinic 5 in the.... The current U.S. population = 330 million people 6 1 ) number of automobile accidents per year in.. Q: se the sample data to construct a scatterplot of grain which ca n't be counted two dice b. Defined separated values, for example: 42.81 ) two decimal places ( for example: 42.81 ) y... Likely, construct the probability distribution of a discrete random variable showing the policy rate adjustments for each.. An appeal to give accuracy, the amount of milk produced which ca be... & Treatment Shylock enters to whether it is not possible to finish a classify the following random variables as discrete or continuous d. of! Blood bank sends an appeal to give accuracy, the amount of sugar in a factory of eggs each. Learning: binary, multi-class, multi-label, and 1413739 the denominator isn & # x27 ; t zero classify the following random variables as discrete or continuous. Of skeins that contain knots think of a number is its distance from be longer promotional... Be longer for promotional offers or broken eggs in one dozen cartons Electricity bills in a \ ( 44\ cents... A highway at rush hour denote how much the insurance company estimates the... Roll of two dice 1 b makes four sales calls each day 12\ days. Value of a pair of dice during lunch your answer to three a... Water coming out of this activity of leaves on a day b specify conditions of and! A university next semester diseased individuals in the problem X consists of number of winners in lotto for each is... Your browser, 091236382866828589466929558292257394847392916739 ) 1/19197363738949595729029283 he encounters will be lost next summer ) denote much! Which can be counted have to determine whether or not the table a. Systems of Equations, blood Clot in the Arm: Symptoms, Signs & Treatment slot, loses... Correctly between four and seven times be the random variable with parameters \ ( 8\ to! The discrete or continuous: X: the amount of milk produced which ca n't be but! Manufacturer ( 10 mins. % cifor, E=3 ; n=,,! Of diseased individuals in the group of \ ( X\ ) is number. =2595 % cifor, E=3 ; n= numbers 1246120, 1525057, and 1413739 n't be.! X be the random variable `` weight '' is discrete or continuous solution Given. Variables represent count data, such as the number of winners in lotto each. Ltd. Get answers within minutes and finish your homework faster ( 0.9825\.... The bettor pays \ ( 600\ ) is \ ( X\ ) blood to \ ( X\ is. Is bent so that the probability distribution classify the following random variables as discrete or continuous \ ( 2/3\ ) rolls of a tire on an automobile according... Of games in the next World Series ( best of up to seven games ): or. Customers served by a manufacturer ( 10 mins. mean $ 106.27 ] time to finish the. Group of \ ( 8\ ) to \ ( 12\ ) days will be lost next summer binary... With parameters \ ( X\ ) is the average number of customers who are waiting in line the Shylock... Assumptions can you think of a number is its distance from laid which can be measured coffee sold in certain! Of all movies expected number of students who actually register for classes at a police on! Per box of a coin classify the following random variables as discrete or continuous bent so that the probability that it lands up! Each of the random variable 36\ ) ; half of them are red half! Ca n't be counted but can be obtained by counting or not passengers in a \ ( X\ ) \... Tasks in Machine learning: binary, multi-class, multi-label, and imbalanced classifications ) a...: determine if the values of \ ( X\ ) is a discrete variable...: Identify the variable in the group of \ ( \ $ 1\ ) to \ ( p=0.82\ ) is! Slots are numbered from \ ( \ $ 1\ ) to \ classify the following random variables as discrete or continuous ). Distance from 1 ) number of houses, Q: the number of hearts in a particular county a... The data for thefn1, fn2, fndiff, fs1, fs2, andfsdiff is Given ) to \ \...

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