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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

Determine probabilities from cumulative distribution functions and cumulative distribution functions from probability density functions, and the reverse
Determine probabilities from probability density functions
A large bakery can produce rolls in lots of either 0, 1000, 2000, or 3000 per day. The production cost per item is $0.10. The demand varies randomly according to the following distribution: demand
A manufacturer stocks components obtained from a supplier. Suppose that 2% of the components are defective and that the defective components occur inde- pendently. How many components must the
An air flight can carry 120 passengers. A pas- senger with a reserved seat arrives for the flight with probability 0.95 Assume the passengers behave inde- pendently. (Computer software is expected.)
Derive the expression for the variance of a geometric random variable with parameter p.
Derive the formula for the mean and standard deviation of a discrete uniform random variable over the range of integersa, a +1.....b.
From 500 customers, a major appliance manufac- turer will randomly select a sample without replacement. The company estimates that 25% of the customers will provide useful data. If this estimate is
Assume the number of errors along a magnetic recording surface is a Poisson random variable with a mean of one error every 10 hits. A sector of data consists of 4096 eight-bit bytes. (a) What is the
Determine the probability mass function for the random variable with the following cumulative distribution function: 70 0.2 x
The random variable X' has the following probability distribution: probability 2 3 5 8 0.2 04 0.3 0.1 (b) P(X >25) Determine the following: (a) P(X 3) (c) P(2.7 <
Messages that arrive at a service center for an in- formation systems manufacturer have been classified on the basis of the number of keywords (used to help route mes- sages) and the type of message,
Determine the constant c so that the following function is a probability mass function: f(x) = cx for x = 1,2,3,4.
Continuation of Exercise 3-163.Determine the minimum number of assemblies that need to be checked so that the probability of at least one defective assembly exceeds 0.95.
Patient response to a generic drug to control pain is scored on a 5-point scale, where a 3 indicates complete relief. Historically, the distribution of scores is 1 2 3 4 5 0.05 0.1 0.2 0.25 0.4 Two
The probability that an individual recovers from an illness in a one-week time period without treatment is 0.1. Suppose that 20 independent individuals suffering from this illness are treated with a
The number of errors in a textbook follows a Poisson distribution with a mean of 0.01 error per page. What is the probability that there are three or less errors in 100 pages?
The number of messages sent to a computer bulletin board is a Poisson random variable with a mean of five mes- sages per hour. (a) What is the probability that five messages are received in 1 hour?
Continuation of Exercise 3-155.(a) What is the probability that you must call six times in order for two of your calls to be answered in less than 30 seconds? (b) What is the mean number of calls to
Continuation of Exercise 3-155.(a) What is the probability that you must call four times to obtain the first answer in less than 30 seconds! (b) What is the mean number of calls until you are
The probability that your call to a service line is an- swered in less than 30 seconds is 0.75. Assume that your calls are independent. (a) If you call 10 times, what is the probability that exactly
Traffic flow is traditionally modeled as a Poisson dis- tribution. A traffic engineer monitors the traffic flowing through an intersection with an average of six cars per minute. To set the timing of
The probability that an eagle kills a jackrabbit in a day of hunting is 10%. Assume that results are independent between days. (a) What is the distribution of the number of days until a sac- cessful
A particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. (a) What is the probability that the
A congested computer network has a 1% chance of losing a data packet and packet losses are independent events. An e-mail message requires 100 packets. (a) What is the distribution of data packets
A total of 12 cells are replicated. Freshly synthesized DNA cannot be replicated again until mitosis is completed. Two control mechanisms have been identified-one positive and one negative-that are
An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per dozen is cracked. Assume each egg load is an inde pendent event. (a) What
Batches that consist of 50 coil springs from a produc- tion process are checked for conformance to customer require ments. The mean number of nonconforming coil springs in a batch is five. Assume
Let X denote the number of bits received in error in a digital communication channel, and assume that X is a binomial random variable with p=0.001. If 1000 bits are transmitted, determine the
The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. am (a) What is the probability of no views in a minute? (b) What is the probability of two or
The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.02 failure per hour. (a) What is the probability that the
The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.05 Blaw per square foot of plastic panel. Assume an automobile interior
The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile. (a) What is the
The number of flaws in bolts of cloth in textile man- ufacturing is assumed to be Poisson distributed with a mean of 0.1 flaw per square meter. (a) What is the probability that there are two flaws in
Data from www.centralhudsonlabs determined the mean number of insect fragments in 225-gram chocolate bars was 14.4, but three brands had insect contamination more than twice the average. See the US.
The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random variable. Assume that on the average there are 10 calls per hour. (a) What is the probability that
Suppose that the number of customers who enter a bank in an hour is a Poisson random variable, and suppose that P(X = 0) = 0.05. Determine the mean and variance of X.
Suppose X has a Poisson distribution with a mean of 0.4. Determine the following probabilities: (a) P(X 0) (c) PX 4) (b) P(X 2) (d) P(X = 8)
Suppose X has a Poisson distribution with a mean of 4.Determine the following probabilities: (a) P(X 0) (b) P(X = 2) (c) PX-4) (d) P(X-8)
Consider the non-failed wells in Exercises 3-31.Assume that four wells are selected randomly (without re- placement) for inspection. (a) What is the probability that exactly two are selected from
(a) Calculate the finite population corrections for Exercises 3-117 and 3-118.For which exercise should the binomial approximation to the distribution of X be better? (b) For Exercise 3-117,
A state runs a lottery in which six numbers are randomly selected from 40, without replacement. A player chooses six numbers before the state's sample is selected. (a) What is the probability that
The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type al of transformation completed: Total Textural Transformation Yes No Total Color Yes
Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards, and 20 are selected without replacement for func- tional testing (a) If
A company employs 800 men under the age of 55.Suppose that 30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure. (a) If 10 men in the company are tested
A batch contains 36 bacteria cells and 12 of the cells are not capable of cellular replication. Suppose you examine three bacteria cells selected at random, without replacement. (a) What is the
Suppose X has a hypergeometric distribution with N = 10, 3, and K = 4.Sketch the probability mass func- tion of X. Determine the cumulative distribution function for X.
Suppose X has a hypergeometric distribution with N=20, 4, and K-4. Determine the following: (a) P(X-1) (b) P(X = 4) (c) P(X 2) (d) Determine the mean and variance of X.
Suppose X has a hypergeometric distribution with N=100, 4, and K 20.Determine the following: (a) P(X = 1) (b) P(X6) (c) P(X=4) (d) Determine the mean and variance of X.
Consider the visits that result in leave without being seen (LWBS) at an emergency department in Example 2-8.Assume that people independently arrive for service at Hospital 1.(a) What is the
Consider the endothermic reactions in Exercise 3-28.Assume independent reactions are conducted. (a) What is the probability that the first reaction to result in a final temperature less than 272 K is
Show that the probability density function of a nega tive binomial random variable equals the probability density function of a geometric random variable when r = 1.Show that the formulas for the
In the process of meiosis, a single parent diploid cell goes through eight different phases. However, only 60% of the processes pass the first six phases and only 40% pass all eight. Assume the
A fault-tolerant system that processes transactions for a financial services firm uses three separate computers. If the operating computer fails, one of the two spares can be im- mediately switched
Assume that 20 parts are checked each hour and that X denotes the number of parts in the sample of 20 that require rework. Parts are assumed to be independent with respect to rework. (a) If the
A trading company has eight computers that it uses to trade on the New York Stock Exchange (NYSE). The probabil- ity of a computer failing in a day is 0.005, and the computers fail independently.
A computer system uses passwords constructed from the 26 letters (a-2) or 10 integers (0-9). Suppose there are 10,000 users of the system with unique passwords. A hacker randomly selects (with
Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial
A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with any opponent is independent of previous encoun ters. The player
In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. (a) What is the probability four
Suppose that X' is a negative binomial random vari- able with p = 0.2 and r = 4.Determine the following: (a) E(X) (c) P(X = 19) (b) P(X=20) (d) P(X = 21) (e) The most likely value for X
Suppose the random variable X has a geometric distribu tion with p=0.5. Determine the following probabilities: (a) P(X) (b) P(X = 4) (c) P(X 8) (d) P(X 2) (e) P(X2)
Consider the endothermic reactions in Exercise 3-28.A total of 20 independent reactions are to be conducted. (a) What is the probability that exactly 12 reactions result in a final temperature less
Assume a Web site changes its content according to the distribution in Exercise 3-30.Assume 10 changes are made independently. (a) What is the probability that the change is made in less than 4 days
Consider the visits that result in leave without being seen (LWBS) at an emergency department in Example 2-8.Assume that four persons independently arrive for service at Hospital 1.(a) What is the
Consider the lengths of stay at a hospital's emergency department in Exercise 3-29.Assume that five persons inde- pendently arrive for service. (a) What is the probability that the length of stay of
A statistical process control chart example. Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in
A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a-2) or 10 integers (0-9). Suppose there are 10,000 users of the system with unique
Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial
An article in Information Security Technical Report ["Malicious Software Past, Present and Future" (2004, Vol. 9, pp. 6-18)] provided the following data on the top ten mali- cious software instances
Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose 15 samples are studied,and they can be considered to be independent for mutation. Determine the following
A particularly long traffic light on your morning com- mute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. (a) Over five mornings, what is
A multiple-choice test contains 25 questions, each with four answers. Assume a student just guesses on each question. (a) What is the probability that the student answers more than 20 questions
Determine the cumulative distribution function of a binomial random variable with = 3 and p = 1/4.
Determine the cumulative distribution function of a binomial random variable with 3 and p = 1/2
Sketch the probability mass function of a binomial distribution with = 10 and p = 0.01 and comment on the shape of the distribution. (a) What value of Xis most likely? (b) What value of X is least
The random variable X has a binomial distribution with = 10 and p = 0.5. Sketch the probability mass function of .X. (a) What value of X' is most likely? (b) What value(s) of X is(are) least likely?
The random variable X has a binomial distribution 10 and p = 0.01. Determine the following proba- with bilities. (a) P(X = 5) (c) P(X = 9) (b) P(X2) (d) P(3X
The random variable X has a binomial distribution with 10 and p=0.5. Determine the following proba- bilities: (a) P(X5) (c) P(X9) (b) P(X2) (d) P(3X
Let X be a binomial random variable with p = 0.1 and n = 10.Calculate the following probabilities from the binomial probability mass function and also from the binomial table in Appendix A and
Let X be a binomial random variable with p = 0.2 and = 20.Use the binomial table in Appendix A to deter- mine the following probabilities. (a) P(X3) (b) P(X>10) (c) P(X = 6) (d) P(6x11)
For each scenario described below, state whether or not the binomial distribution is a reasonable model for the random variable and why. State any assumptions you make. (a) A production process
Show that for a discrete uniform random variable .X, if each of the values in the range of X is multiplied by the constantc, the effect is to multiply the mean of X by c and the variance of X by .
Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 675 to 700 m. (a) What is the mean and variance of
The lengths of plate glass parts are measured to the nearest tenth of a millimeter. The lengths are uniformly dis- tributed, with values at every tenth of a millimeter starting at 590.0 and
Product codes of two, three, four, or five letters are equally likely. What is the mean and standard deviation of the number of letters in the codes?
Let the random variable X have a discrete uniform distribution on the integers 15x3. Determine the mean and variance of .X.
Calculate the mean and variance for the random variable in Exercise 3-31.
Calculate the mean and variance for the random variable in Exercise 3.30.
Calculate the mean and variance for the random variable in Exercise 3.29.
Calculate the mean and variance for the random variable in Exercise 3.28.
An article in the Journal of Database Management ["Experimental Study of a Self-Tuning Algorithm for DBMS Buffer Pools (2005, Vol. 16, pp. 1-20)] provided the workload used in the TPC-C OLTP
Trees are subjected to different levels of carbon dioxide atmosphere with 6% of the trees in a minimal growth condition at 350 parts per million (ppm), 10% at 450 ppm (slow growth). 47% at 550 ppm
The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent com- puters working in parallel. At each critical step, the comput- ers "vote" to determine
In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states. Assume the following proportions of the states: Nickel Charge 0
Determine the mean and variance of the random variable in Exercise 3-18
Determine the mean and variance of the random variable in Exercise 3.16.
Determine the mean and variance of the random variable in Exercise 3.14.
Determine the cumulative distribution function for the random variable in Exercise 3-16; also determine the following probabilities: (a) PX1.5) (b) P(X3) (c) PX2) (d) P1 Determine each of the
Determine the cumulative distribution function for the random variable in Exercise 3-15; also determine the fol- lowing probabilities: (a) P(X1.25) (b) P(X2.2) (c) P(-1.1 0)

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