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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

Construct a histogram for the female student height data in Exercise 6.46.
Construct a histogram for the energy consumption data in Exercise 6.29.
Construct histograms with 8 and 16 bins for the data in Exercise 6-24.Compare the histograms. Do both his- tograms display similar information?
Construct histograms with 8 and 16 bins for the data in Exercise 6-23.Compare the histograms. Do both his- tograms display similar information?
Construct frequency distributions and histograms with 8 bins and 16 bins for the motor fuel octane data in Exercise 6.22. Compare the histograms. Do both histograms display similar information?
Construct a frequency distribution and histogram for the yield data in Exercise 6.25.
Construct a frequency distribution and histogram for the cotton content data in Exercise 6.24.
Construct a frequency distribution and histogram us- ing the failure data from Exercise 6.23.
Construct a frequency distribution and histogram for the motor fuel octane data from Exercise 6-22.Use eight bins.
The net energy consumption (in billions of kilowatt- hours) for countries in Asia in 2003 was as follows (source: U.S. Department of Energy Web site, http://www.cia.doc.gov/meu). Construct a
Calculate the sample median, mode, and mean for the data in Exercise 6-24.Explain how these three measures of location describe different features of the data.
Calculate the sample median, mode, and mean of the data in Exercise 6-23.Explain how these three measures of location describe different features in the data.
Calculate the sample median, mode, and mean of the data in Exercise 6-22.Explain how these three measures of location describe different features of the data.
The following data are the joint temperatures of the O-rings ("F) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger
An article in the Journal of Aircraft (1988) described the computation of drag coefficients for the NASA 0012 airfoil. Different computational algorithms were used at M = 0.7 with the following
The pH of a solution is measured eight times by one op- erator using the same instrument. She obtains the following data: 7.15, 7.20, 7.18.7.19, 7.21, 7.20, 7.16, and 7.18.Calculate the sample mean
An article in the Journal of Physiology ["Response of Rat Muscle to Acute Resistance Exercise Defined by Transcriptional and Translational Profiling" (2002, Vol. 545.pp. 27-41)] studied gene
Preventing fatigue crack propagation in aircraft struc- tures is an important element of aircraft safety. An engineering study to investigate fatigue crack in a 9 cyclically loaded wing boxes
The April 22, 1991, issue of Aviation Week and Space Technology reported that during Operation Desert Storm, US. Air Force F-117A pilots flew 1270 combat sorties for a total of 6905 hours. What is
The following data are direct solar intensity measure- ments (watts/m) on different days at a location in southern Spain: 562,869, 708, 775,775, 704, 809, 856, 655, 806, 878, 909, 918, 558, 768, 870,
Can the sample standard deviation be equal to zero? Give an example.
For any set of data values, is it possible for the sample standard deviation to be larger than the sample mean? Give an example.
Know how to use simple time series plots to visually display the important features of timeoriented data
Explain how to use box plots and other data displays to visually compare two or more samples of data
Construct and interpret normal probability plots
Explain the concept of random sampling
Construct and interpret visual data displays, including the stem-and-leaf display, the histogram, and the box plot
Explain the concepts of sample mean, sample variance, population mean, and population variance
Compute and interpret the sample mean, sample variance, sample standard deviation, sample median, and sample range
A marketing company performed a risk analysis for a manufacturer of synthetic fibers and concluded that new com- petitors present no risk 13% of the time (due mostly to the diversity of fibers
An order of 15 printers contains four with a graphics-enhancement feature, five with extra memory, and six with both features. Four printers are selected at random, without replacement, from this
A small company is to decide what investments to use for cash generated from operations. Each investment has a mean and standard deviation associated with the percentage gain. The first security has
The permeability of a membrane used as a moisture barrier in a biological application depends on the thickness of three integrated layers. Layers 1, 2, and 3 are normally dis- tributed with means of
The permeability of a membrane used as a moisture barrier in a biological application depends on the thickness of two integrated layers. The layers are normally distributed with means of 0.5 and 1
To evaluate the technical support from a computer manufacturer, the number of rings before a call is answered by a service representative is tracked. Historically, 70% of the calls are answered in
The backoff torque required to remove bolts in a steel plate is rated as high, moderate, or low. Historically, the prob ability of a high, moderate, or low rating is 0.6, 0.3, or 0.1, respectively.
The percentage of people given an antirheumatoid medication who suffer severe, moderate, or minor side effects are 10, 20, and 70%, respectively. Assume that people react independently and that 20
Show that the following function satisfies the proper- ties of a joint probability mass function: 0 f(x,y) 1/4 1/8 0 1/8 1 1/4 2 1/4 Determine the following: (a) P(X < 0.5, y < 1.5) (c) P(X 0.5, Y
The random variable X' has the probability distri- bution x(x)=0x54 Find the probability distribution of Y = (X-2). Supplemental Exercises
Suppose that X has the probability distribution 1x(x)=1. 15x2 Find the probability distribution of the random variable y=
The velocity of a particle in a gas is a random variable I'with probability distribution Jr(v) = are where b is a constant that depends on the temperature of the gas and the mass of the particle. (a)
A random variable X has the following probability distribution: 1x(x)= x20 (a) Find the probability distribution for Y = x. (b) Find the probability distribution for Y (c) Find the probability
Suppose that Xhas a uniform probability distribution f(x)=1 0xsl Show that the probability distribution of the random variable y= -2 In X is chi-squared with two degrees of freedom.
Suppose that X is a continous random variable with probability distribution f(x)=0x6 (a) Find the probability distribution of the random variable y=2x+10. (b) Find the expected value of Y.
Let X be a binomial random variable with p = 0.25 and = 3.Find the probability distribution of the random variable Y=X
The photoresist thickness in semiconductor manufac turing has a mean of 10 micrometers and a standard deviation of I micrometer. Assume that the thickness is normally distributed and that the
The width of a casing for a door is normally distrib- uted with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23-7/8 inches and
Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time of firing are normally distributed random variables with means of 40 min
If X and Y have a bivariate normal distribution with joint probability density f(x,y; Pop), show that the marginal probability distribution of X is normal with mean Hy and standard deviation of
Show that the probability density function f(x,y dsds, sp) of a bivariate normal distribution integrates to one. [Hiar: Complete the square in the exponent and use the fact that the integral of a
Suppose that X and Y have a bivariate normal distri- bution with joint probability density function f(x,y,p (a) Show that the conditional distribution of Y. given that X=x, is normal. (b) Determine
In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Let X and Y denote the milliliters of acid and base needed for
Suppose X and Y have a bivariate normal distribution (c) p=-0.8 with a = 0.04,, = 0.08, Determine the following: (a) P(2.95 <
Four electronic ovens that were dropped during ship- ment are inspected and classified as containing either a major, a minor, or no defect. In the past, 60% of dropped ovens had a ma- jor defect, 30%
A Web site uses ads to route visitors to one of four land- ing pages. The probabilities for each landing page are equal.. Consider 20 independent visitors and let the random variables W. X, Y, and Z
Based on the number of voids, a ferrite slab is classi- fied as either high, medium, or low. Historically, 5% of the slabs are classified as high, 85% as medium, and 10% as low. A sample of 20 slabs
Test results from an electronic circuit board indicate that 50% of board failures are caused by assembly defects, 30% are due to electrical components, and 20% are due to me- chanical defects.
Determine the value for c and the covariance and cor- relation for the joint probability density function f(x,y) = exy over the range
For the Transaction Processing Performance Council's benchmark in Exercise 5-10, let X, Y, and Zdenote the average number of selects, updates, and inserts operations required for each type
Determine the covariance and correlation for X, and Xin the joint distribution of the multinomial random vari- ables X. X, and X, with p = p = p = , and n = 3.What can you conclude about the sign of
Determine the covariance and correlation for the joint probability distribution shown in Fig. 5-10(a) and described in Example 5-10.
Determine the value for c and the covariance and correlation for the joint probability mass function fix(x, y) = c(x+y) for x 1,2,3 and y = 1,2,3.
Determine the covariance and correlation for the following joint probability distribution: -1 -0.5 0.5 3 -1 1 2 L(x,y) 1/8 1/4 1/2 1/8
Determine the covariance and correlation for the following joint probability distribution: 1 1 2 4 y 3 4 5 6 In(x,y) 1/8 1/4 1/2 1/8
A manufacturer of electroluminescent lamps knows that the amount of luminescent ink deposited on one of its products is normally distributed with a mean of 1.2 grams and a standard deviation of 0.03
The weights of adobe bricks used for construction are normally distributed with a mean of 3 pounds and a standard deviation of 0.25 pound. Assume that the weights of the bricks are independent and
The yield in pounds from a day's production is normally distributed with a mean of 1500 pounds and standard deviation of 100 pounds. Assume that the yields on different days are independent random
Suppose the random variables X, Y, and Z have the joint probability density function f(x, y, z) = 8xyz for 0 0.y>0, > 0, and x+y+
Two methods of measuring surface smoothness are used to evaluate a paper product. The measurements are recorded as deviations from the nominal surface smoothness in coded units. The joint probability
The conditional probability distribution of Y given X = x is frix(y)=xe for y> 0, and the marginal probability distribution of X is a continuous uniform distribu- tion over 0 to 10.(a) Graph
Determine the value of e that makes the function f(x,y) = cry a joint probability density function over the range 0(c) P(Y3) (c) E(X) (g) (d) P(X
Determine the value of e that makes the function f(x, y) = c(x + y) a joint probability density function over the range 0 2X 1) (k) Conditional probability distribution of X given that Y 5 2
Determine the value of c such that the function f(x, y) = cxy for 0 18,1 <
In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that
For the Transaction Processing Performance Council's benchmark in Exercise 5-10, let X, Y, and Z denote the average number of selects, updates, and inserts opera- tions required for each type of
An article in the Journal of Database Manage- ment ["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
An engineering statistics class has 40 students and 60% are electrical engineering majors, 10% are industrial engineering majors, and 30% are mechanical engineering majors. A sample of four students
Suppose the random variables X, Y, and Z have the following joint probability distribution. fx.=) 0.05 2 0.10 0.15 2 0.20 0.20 2 2 2 0.15 0.10 2 2 2 0.05 Determine the following: (a) P(X 2) (c) P(Z
Show that the following function satisfies the proper- ties of a joint probability mass function. y 1x(x-3) -2 1/8 -0.5 1/4 0.5 1 1/2 1 2 1/8 devices 1 and 2, respectively. Assume the devices are
Show that the following function satisfies the proper. ties of a joint probability mass function. 1x(x-3) 1 1/4 1.5 2 1/8 1.5 3 1/4 2.5 4 1/4 3 5 1/8 Determine the following: (a) PX 2.5.Y
Determine the distribution of a general function of a random variable
Calculate means and variances for linear combinations of random variables and calculate probabilities for linear combinations of normally distributed random variables
Understand properties of a bivariate normal distribution and be able to draw contour plots for the probability density function
Use the multinomial distribution to determine probabilities
Interpret and calculate covariances and correlations between random variables
Calculate marginal and conditional probability distributions from joint probability distributions
Use joint probability mass functions and joint probability density functions to calculate probabilities
A process is said to be of six-sigma quality if the process mean is at least six standard deviations from the nearest specification. Assume a normally distributed measurement.(a) If a process mean is
Lack of Memory Property. Show that for an exponential random variable X, PX 1) = P(X
Let the random variable X denote a measure- ment from a manufactured product. Suppose the target value for the measurement is w. For example, X could denote a dimensional length, and the target might
A bearing assembly contains 10 bearings. The bearing diameters are assumed to be independent and normally distributed with a mean of 1.5 millimeters and a standard deviation of 0.025 millimeter. What
The steps in this exercise lead to the probabil- ity density function of an Erlang random variable X' with parameters and r, f(x) = x'x '^(-1),x>0. and = 1,2..... (a) Use the Poisson distribution to
Continuation of Exercise 4-176.Rework parts (a) and (b). Assume that the lifetime is a lognormal random vari- able with the same mean and standard deviation
Continuation of Exercise 4-176.Rework parts (a) and (b). Assume that the lifetime is an exponential random variable with the same mean.
The life of a semiconductor laser at a constant power is normally distributed with a mean of 7000 hours and a stan dard deviation of 600 hours. (a) What is the probability that a laser fails before
Continuation of Exercise 4-174.Assume that the standard deviation of the size of a dot is 0.0004 inch. If the probability that a dot meets specifications is to be 0.9973, what specifications are
Suppose that X has a lognormal distribution with parameters = 0 and = 4.Determine the following: (a) P(10X50) (b) The value for x such that PX(e) The covering thickness of 95% of samples is below
The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. You have owned this CPU for three years.(a) What is the probability that the CPU
The time between calls is exponentially distributed with a mean time between calls of 10 minutes. (a) What is the probability that the time until the first call is less than 5 minutes? (b) What is
Suppose that f(x)=05x-1 for 2 3) (c) P(2.5 <

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