Basics of Statistics Questions & Answers
- Q: * Suppose a fair die is rolled n times. By using the indicator variable method, find the expected value of the number of faces that appear exactly twice. Now compute the expected value with n D 2; 3; 5; 10; and 20. Q Posted 3 months ago
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- Q: * (Waiting Time). An urn contains four red and four green balls, which are taken out without replacement, one at a time, at random. Let X be the first draw at which a green ball is taken out. Find the pmf and the expected value of X. Hint: Try to use... Posted 3 months ago
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- Q: * (Longest Run). Suppose a fair coin is tossed five times. Find the pmf of the longest run, either of heads or of tails, and compare it with the pmf of the longest head run worked out in the text. Make a comment on what you learn from the comparison.... Posted one year ago
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- Q: By using the indicator variable method, find the expected value of the total number of hearts in the hands of North and South combined in a bridge game. Does the expected value make sense intuitively? Q Posted 3 months ago
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- Q: * (A Two-Stage Experiment). Suppose a fair die is rolled once and the number observed is N. Then a fair coin is tossed N times. Let X be the number of heads obtained. Find the pmf, the CDF, and the expected value of X. Does the expected value make... Posted one year ago
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- Q: A motorist encounters four consecutive traffic lights, each equally likely to be red or green. Let X be the number of green lights passed by the motorist before being stopped by a red light. What is the pmf of X? Q Posted 6 months ago
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- Q: Find the pmf and the CDF of the number of heads obtained in four tosses of a fair coin and plot the CDF. Suppose a fair die is rolled twice and that X is the absolute value of the difference of the two rolls. Find the pmf and the CDF of X and plot... Posted 2 years ago
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- Q: (Use Your Computer). Simulate the airplane reliability problem, taking it to be a three-out-of-four system and taking the reliability of each individual engine to be .99. Perform the simulation 1000 times, and count how many times, if any, the plane... Posted 3 months ago
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- Q: (Casino Slot Machines). A typical slot machine in a casino has three wheels, each marked with 20 symbols spaced equally around the wheel. The machine is constructed so that on each play the three wheels spin independently, and each wheel is equally... Posted 2 years ago
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- Q: (Polygraphs). Polygraphs are routinely administered to job applicants for sensitive government positions. Suppose someone actually lying fails the polygraph 90% of the time but someone telling the truth also fails the polygraph 15% of the time. If a... Posted one year ago
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- Q: Of the paintings in a certain gallery, 25% are not original. A certain collector makes an error in judging an item’s authenticity 15% of the time, whether the painting is an original or not. If she purchases an item believing that it is an... Posted 3 months ago
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- Q: A true-false question will be posed to a couple on a game show. The husband and the wife each pick the correct answer with probability p. Should the couple decide to let one of them answer the question or decide that they will give the common answer... Posted 2 years ago
- Q: A statistics department has five assistant professors, two associate professors, and six full professors. Two of these 13 faculty members are chosen at random. What is the probability that the junior member is an assistant professor if the senior... Posted one year ago
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- Q: * The probability that a coin will show all heads or all tails when tossed four times is .25. What is the probability that it will show two heads and two tails? Sam tosses two fair dice and Fred tosses one. Sam wins if his sum is at least twice as... Posted 3 months ago
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- Q: * In a country, 60% of parents have one child, 30% have two children, and 10% have three children. A randomly chosen child turns out to be a boy. What is the probability that he has no older brother? * A fair die is tossed repeatedly until every face... Posted 4 months ago
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- Q: On a table there is a double-headed coin and there is a fair coin. One of them was randomly chosen and tossed, and the outcome was a head. What is the probability that the lower side of this coin is a tail? Two distinct cards are drawn one at a time... Posted 3 months ago
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- Q: Jen will call Cathy on Saturday with a 60% probability. She will call Cathy on Sunday with an 80% probability. The probability that she will call on neither of the two days is 10%. What is the probability that she will call on Sunday if she calls on... Posted one year ago
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- Q: (Use Your Computer). Simulate the birthday problem with n D 30; 60; 100 people. Perform 500 simulations, and count how many times you got: (a) at least one pair of people with a common birthday; (b) at least two different pairs of people with two... Posted 3 months ago
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- Q: * Suppose n unrelated families, defined as the husband, the wife, and one child, are gathered together. What is the smallest n for which chances are > 50% that there will be two or more families completely matched in birthdays (i.e., the two husbands... Posted 3 months ago
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- Q: Suppose n unrelated people are gathered together. What is the smallest n for which chances are >50% that there will be two or more people born in the same calendar month? Q Posted one year ago
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- Q: * (The Rumor Problem). In a town with n residents, someone starts a rumor by saying it to one of the other n - 1 residents. Thereafter, each recipient passes the rumor on to one of the other residents, chosen at random. What is the probability that... Posted one year ago
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- Q: * n people are lined up at random for a photograph. What is the probability that a specified set of r people happen to be next to each other? Mark and his wife, with n other people, are lined up at random for a photograph. What is the probability... Posted 2 years ago
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- Q: * (The General Shoes Problem). There are n pairs of shoes of n distinct colors in a closet and 2m are pulled out at random from the 2n shoes. What is the probability that there is at least one complete pair among the shoes pulled? Find the... Posted 9 months ago
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- Q: * (Coincidence). Suppose each of n sticks are broken into two pieces, one longer than the other. Then the 2n pieces are paired up to make n new sticks. Find the probabilities that the pieces are all paired up in their original order and that each... Posted 11 months ago
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- Q: * (Logic). Suppose six customers stand in line at a box office, three with five-dollar bills and three with ten-dollar bills. Suppose each ticket costs 5 dollars, and the box office has no money initially. What is the probability that none of the... Posted 2 years ago
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- Q: (Bad Luck). Jeff and Donna have three children. Two are chosen at random on each day of the week to help with the dishes. What is the probability that at least one child gets chosen every day of the week? (Check Your Intuition). An urn contains three... Posted 11 months ago
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- Q: (Coincidence, Again). Four men throw their watches into the sea, and the sea brings back to each man at random one watch. What is the probability that exactly one man gets his own watch back? A fair die is rolled thrice. What is the probability that... Posted 2 years ago
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- Q: (A Problem of Tom Sellke). Suppose that cards are picked at random from a full deck of 52 cards. (a) What is the probability that exactly one jack, one queen, and one king have been picked from the deck when the first ace turns up? (b) What is the... Posted one year ago
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- Q: In a building with six floors, an elevator starts with four people at the ground floor. What is the probability that the four people get off at exactly two floors? An urn contains five red, five black, and five white balls. If three balls are chosen... Posted 2 years ago
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- Q: (Odd Man Out). Each of three people toss a coin. What is the probability of someone being the “odd man out”? This means that two of them obtain an identical outcome, while the odd man gets a different one. Q Posted 2 years ago
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- Q: Consider the experiment of tossing a coin three times. Give verbal descriptions for the following events: (a) {HHH; HHT; HTH; HTTg}. (b) {HHH; HHT; HTH; THHg}. (c) (HHT; HHH; TTH; TTTg}. (d) {HTH; HTT; TTT; TTHg}. Q Posted 2 years ago
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- Q: (Skills Exercise). Let E ;F, and G be three events. Find expressions for the following events: (a) only E occurs; (b) both E and G occur, but not F; (c) all three occur; (d) at least one of the events occurs; (e) at most two of them occur. Q Posted one year ago
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- Q: (Skills Exercise). Events A; B, and C are defined in a sample space . Find expressions for the following probabilities in terms of P. A/; P. B/; P .C /; P. AB/; P .AC /; P. BC /, and P .ABC /; here AB means A \ B, etc.: (a) the probability that... Posted 2 years ago
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- Q: Mark goes out to dinner twice a week. If he chooses the days to go out at random, what is the probability that he goes out on exactly one weeknight? The population of Danville is 20,000. Can it be said with certainty that there must be two or more... Posted 2 years ago
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- Q: Suppose Mark pulls a coin from his pocket and tosses it four times and always obtains a tail. But the coin looks normal. Would you start to suspect that Mark pulled a biased coin? A telephone number consists of ten digits, of which the first digit is... Posted 3 months ago
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- Q: There is very good reason to challenge any behaviour from practitioners that would raise serious concerns if those adults were within a child’s own family. Practitioners have a duty of care as well as obligations about genuine child protection.... Posted 3 months ago
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- Q: This private nursery and others within the same chain have promoted access to the nursery webcam facility as a way for parents to join in their child’s day. The baby-room team has reached an awkward position with one parent. Darren’s... Posted 3 months ago
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- Q: Staff and parents are keen for the children to learn to swim and groups are walked to the nearby leisure centre. Several children say that they do not like the swimming coach, that he is ‘horrid’ and ‘shouts all the time’.... Posted 3 months ago
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- Q: Children very rarely lie about abuse. They are far more likely to have difficulty in telling you, especially if the person harming them is part of their family or a respected authority figure. But it is possible that a child may give an account of... Posted 3 months ago
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- Q: Tackling obesity is a public health issue and should in the fi rst instance be tacked as such. Interventions to address obesity are part of the Healthy Child Programme (Department of Health, 2009). Rudolph (2009) provides useful guidance and a... Posted 3 months ago
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- Q: Professional (or organisational) dangerousness: when inappropriate values, priorities or methods lead professionals to act in ways that fail to reduce the risk to children or young people. The full reports of research reviews can be long, but many of... Posted one year ago
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- Q: During the morning break, in the playground of the school where you work, you watched a vigorous physical game between the eight-year-olds that gradually began to concern you. The game involved a lot of shrieking and chasing in which the boys and... Posted 3 months ago
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- Q: Who do you think is more likely to physically abuse children – females or males? It is worth noting that children are more likely to be maltreated by females than males (See Corby et al. (2012: 108). However, in situations of physical abuse,... Posted 9 months ago
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- Q: Scapegoating: a process by which an adult or child is made to feel personally responsible for the distress or deep dissatisfaction felt by others, and this judgement is not an accurate refl ection of the true situation. Students on placement at Pike... Posted 3 months ago
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- Q: Compare break-even analysis and sensitivity analysis. How does a data table help you perform what-if analysis? What is the difference between a one-variable data table and a two-variable data table? When would you use each type of data table? Posted 9 months ago
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- Q: _____ The lookup_value of a HLOOKUP function can be a contiguous cell range. _____ In a VLOOKUP formula with a TRUE lookup type, the first column of the lookup table referenced must be in ascending order to retrieve the correct value. _____ The... Posted 4 months ago
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- Q: What formula could you write to calculate the mean of the following data set: 4, 10, 8, 6, 2, 4, 14? (Note that a resulting value is not required.) What is the median value of the data set given in Question 1? What is the mode of the data set given... Posted 3 months ago
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- Q: Smoking and personality A study about smoking and personality (by A. Terracciano and P. Costa, Addiction, vol. 99, 2004, pp. 472–481) used a sample of 1638 adults in the Baltimore Longitudinal Study on Aging. The subjects formed three groups... Posted 3 months ago
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- Q: Movie recommendation In a quick poll at the exit of a movie theater, 8 out of 12 randomly polled viewers said they would recommend the movie to their friends. a. Construct an appropriate 95% confidence interval for the population proportion. b. Is it... Posted 2 years ago
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- Q: Do students like statistics? All respondents out of a random sample of ten students in a college said that they like statistics. Now you want to estimate the proportion of students who like statistics in the whole college. a. Find the sample... Posted 3 months ago
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- Q: Web survey to get large n A newspaper wants to gaugepublic opinion about legalization of marijuana. The sample size formula indicates that it need a random sample of 875 people to get the desired margin of error. But surveys cost money, and it... Posted 2 years ago
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