Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
Problem 1E Show that the following function satisfies the properties of a joint probability mass function. x y 1.0 1 1/4 1.5 2 1/8 1.5 3 1/4 2.5 4 1/4 3.5 5 1/8

Applied Statistics and Probability for Engineers 6
Determine the value of c that makes the function \(f(x, y)=c(x+y)\) a joint probability mass function over the nine points with x = 1,2,3 and y = 1,2,3. Determine the following: (a) \(P(X=1, Y<4)\) (b) ) \(P(X=1)\) (c) \(P(Y=2)\) (d) ) \(P(X<2,

Applied Statistics and Probability for Engineers 6
Show that the following function satisfies the properties of a joint probability mass function. Determine the following: (a) \(P(X<0.5, Y<1.5)\) (b) \(P(X<0.5)\) (c) \(P(Y<1.5)\) (d) \(P(X>0.5, Y<4.5)\) (e) \(E(X), E(Y), V(X)\), and \(V(Y)\) (f) Marginal probability distribu

Applied Statistics and Probability for Engineers 6
Problem 4E Four electronic printers are selected from a large lot of damaged printers. Each printer is inspected and classified as containing either a major or a minor defect. Let the random variables X and Y denote the number of printers with major and minor defects, respectively. Determine the ra

Applied Statistics and Probability for Engineers 6
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bit

Applied Statistics and Probability for Engineers 6
A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively. A sample of four pages is selected without replacement, and X and Y denote the number of pages with moderate and high graphics output in the sample. Determine

Applied Statistics and Probability for Engineers 6
A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for

Applied Statistics and Probability for Engineers 6
Suppose that the random variables X, Y , and Z have the following joint probability distribution. Determine the following: (a) P(X = 2) (b) P(X = 1,Y = 2) (c) P(Z < 1.5) (d) P(X = 1 or Z = 2) (e) E(X)

Applied Statistics and Probability for Engineers 6
An engineering statistics class has 40 students; 60% are electrical engineering majors, 10% are industrial engineering majors, and 30% are mechanical engineering majors. A sample of four students is selected randomly without replacement for a project team. Let X and Y denote the number of industrial

Applied Statistics and Probability for Engineers 6
2q3An article in the Journal of Database Management [Experimental Study of a Self-Tuning Algorithm for DBMS Buffer Pools (2005, Vol. 16, pp. 120)] provided the workload used in the TPC-C OLTP (Transaction Processing Performance Councils Version C On-Line Transaction Processing) benchmark, which simul

Applied Statistics and Probability for Engineers 6
For the Transaction Processing Performance Councils benchmark in Exercise 5-10, let X, Y , and Z denote the average number of selects, updates, and inserts operations required for each type of transaction, respectively. Calculate the following: (a) \(f_{x y z}(x, y, z)\) (b) Conditional probability m

Applied Statistics and Probability for Engineers 6
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 the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits

Applied Statistics and Probability for Engineers 6
Determine the value of c such that the function f(x,y) = cxy for 0 < x < 3 and 0 < y < 3 satisfies the properties of a joint probability density function. Determine the following: (a) P(X < 2, Y < 3) (b) P(X < 2.5) (c) P(1 < Y < 2.5) (d) P(X > 1.8, 1 < Y < 2.5) (e) E(X) (f

Applied Statistics and Probability for Engineers 6
Determine the value of c that makes the function \(f(x, y)=c(x+y)\) a joint probability density function over the range 0 < x < 3 and 0 < y < x. Determine the following: (a) \(P(X<1, Y<2)\) (b) \(P(1<x<2)\) (c) \(P(Y>1)\) (d) \(P(X<2, Y<2)\) (e)

Applied Statistics and Probability for Engineers 6
Determine the value of c that makes the function \(f(x, y)=c(x+y)\) a joint probability density function over the range 0 < x < 3 and 0 < y < x. Determine the following: (a) \(P(X<1, Y<2)\) (b) \(P(1<x<2)\) (c) \(P(Y>1)\) (d) \(P(X<2, Y<2)\) (e)

Applied Statistics and Probability for Engineers 6
Determine the value of c that makes the function \(f(x, y)=c e^{-2 x-3 y}\) a joint probability density function over the range \(0<x \text { and } .0<y<x\) Determine the following: (a) \(P(X<1, Y<2)\) (b) \(P(1<X<2)\) (c) \(P(Y>3)\) (d) \(P(X<2, Y<2)\) (e) \(E(X)\)

Applied Statistics and Probability for Engineers 6
Determine the value of c that makes the function \(f(x, y)=c e^{-2 x-3 y}\), a joint probability density function over the range 0 < x and x < y. Determine the following: (a) \(P(X<1, Y<2)\) (b) \(P(1<X<2)\) (c) \(P(Y>3)\) (d)

Applied Statistics and Probability for Engineers 6
The conditional probability distribution of Y given X = x is \(f_{Y \mid x}(y)=x e^{-x y}\) for \(y>0\), and the marginal probability distribution of X is a continuous uniform distribution over 0 to 10. (a) Graph \(f_{Y \mid x}(y)=x e^{-x y}\) for \(y>0\) for several values of x. Determine: (b

Applied Statistics and Probability for Engineers 6
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 distribution of the two measurements is a uniform distribution over the region \(0<x<4,0<y\), and \(x

Applied Statistics and Probability for Engineers 6
The time between surface finish problems in a galvanizing process is exponentially distributed with a mean of 40 hours. A single plant operates three galvanizing lines that are assumed to operate independently. (a) What is the probability that none of the lines experiences a surface finish problem in

Applied Statistics and Probability for Engineers 6
A popular clothing manufacturer receives Internet orders via two different routing systems. The time between orders for each routing system in a typical day is known to be exponentially distributed with a mean of 3.2 minutes. Both systems operate independently. (a) What is the probability that no ord

Applied Statistics and Probability for Engineers 6
The blade and the bearings are important parts of a lathe. The lathe can operate only when both of them work properly. The lifetime of the blade is exponentially distributed with the mean three years; the lifetime of the bearings is also exponentially distributed with the mean four years. Assume that

Applied Statistics and Probability for Engineers 6
Suppose that the random variables X, Y , and Z have the joint probability density function \(f(x, y, z)=8 x y z\) for 0 < x 1,0 < y < 1, and 0 < z < 1. Determine the following: (a) \(P(X<0.5)\) (b) \(P(<0.5, Y<0.5)\) (c) \(P(Z<2)\) (d) \(P(X=0.5\) or \(Z<2)\) (

Applied Statistics and Probability for Engineers 6
Suppose that the random variables X, Y , and Z have the joint probability density function \(f x, x y z(y, z c)=\) over the cylinder \(x^{2}+y^{2}<4\) and \(0<z<4\). Determine the constant c so that fxyz(x,y,z) is a probability density function. Determine the following: (a) \(P\left(X^{2}+Y^{2}<2\rig

Applied Statistics and Probability for Engineers 6
Determine the value of c that makes \(f x y z(x, y, z)=c\) a joint probability density function over the region \(x>0, y>0, z>0\), and \(x+y+z<1\). Determine the following: (a) \(P(X<0.5, Y<0.5, Z<0.5)\) (b) \(P(X<0.5, Y<0.5)\) (c) \(P(X<0.5)\) (d) \(E(X)\) (e) Margina

Applied Statistics and Probability for Engineers 6
Problem 26E The yield in pounds from a days 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 variables. (a) What is the probability that the production yield exceeds 1400 pounds on eac

Applied Statistics and Probability for Engineers 6
Problem 27E 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 that a random sample of 20 bricks is selected. (a) What is the probability that all the br

Applied Statistics and Probability for Engineers 6
Problem 28E 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 gram. Any lamp with less than 1.14 grams of luminescent ink fails to meet customers spec

Applied Statistics and Probability for Engineers 6
The lengths of the minor and major axes are used to summarize dust particles that are approximately elliptical in shape. Let X and Y denote the lengths of the minor and major axes (in micrometers), respectively. Suppose that fx(X) = exp(-x), 0 < x and the conditional distribution fY|x(y) = exp[-(y-x)

Applied Statistics and Probability for Engineers 6
An article in Health Economics [Estimation of the Transition Matrix of a Discrete-Time Markov Chain (2002, Vol.11, pp. 3342)] considered the changes in CD4 white blood cell counts from one month to the next. The CD4 count is an important clinical measure to determine the severity of HIV infections. T

Applied Statistics and Probability for Engineers 6
The systolic and diastolic blood pressure values (mm Hg) are the pressures when the heart muscle contracts and relaxes (denoted as Y and X, respectively). Over a collection of individuals, the distribution of diastolic pressure is normal with mean 73 and standard deviation 8. The systolic pressure is