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.
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2-1
SAMPLE SPACES AND EVENTS
2-2
INTERPRETATIONS OF PROBABILITY
2-3
ADDITION RULES
2-4
CONDITIONAL PROBABILITY
2-5
MULTIPLICATION AND TOTAL PROBABILITY RULES
2-6
INDEPENDENCE
2-7
BAYES THEOREM
2-8
RANDOM VARIABLES
3-1
DISCRETE RANDOM VARIABLES
3-2
PROBABILITY DISTRIBUTIONS AND PROBABILITY MASS FUNCTIONS
3-3
CUMULATIVE DISTRIBUTION FUNCTIONS
3-4
MEAN AND VARIANCE OF A DISCRETE RANDOM VARIABLE
3-5
DISCRETE UNIFORM DISTRIBUTION
3-6
BINOMIAL DISTRIBUTION
3-7
GEOMETRIC AND NEGATIVE BINOMIAL DISTRIBUTIONS
3-8
HYPERGEOMETRIC DISTRIBUTION
3-9
POISSON DISTRIBUTION
4-10
ERLANG AND GAMMA DISTRIBUTIONS
4-11
WEIBULL DISTRIBUTION
4-12
LOGNORMAL DISTRIBUTION
4-2
PROBABILITY DISTRIBUTIONS AND PROBABILITY DENSITY FUNCTIONS
4-3
CUMULATIVE DISTRIBUTION FUNCTIONS
4-4
MEAN AND VARIANCE OF A CONTINUOUS RANDOM VARIABLE
4-5
CONTINUOUS UNIFORM DISTRIBUTION
4-6
NORMAL DISTRIBUTION
4-7
NORMAL APPROXIMATION TO THE BINOMIAL AND POISSON DISTRIBUTIONS
4-8
CONTINUITY CORRECTIONS TO IMPROVE THE APPROXIMATION
4-9
EXPONENTIAL DISTRIBUTION
5-1
TWO DISCRETE RANDOM VARIABLES
5-10
CHEBYSHEVS INEQUALITY (CD ONLY)
5-2
MULTIPLE DISCRETE RANDOM VARIABLES
5-3
TWO CONTINUOUS RANDOM VARIABLES
5-4
MULTIPLE CONTINUOUS RANDOM VARIABLES
5-5
COVARIANCE AND CORRELATION
5-6
BIVARIATE NORMAL DISTRIBUTION
5-7
LINEAR COMBINATIONS OF RANDOM VARIABLES
5-8
FUNCTIONS OF RANDOM VARIABLES (CD ONLY)
5-9
MOMENT GENERATING FUNCTIONS (CD ONLY)
6-1
DATA SUMMARY AND DISPLAY
6-3
STEM-AND-LEAF DIAGRAMS
6-4
FREQUENCY DISTRIBUTIONS AND HISTOGRAMS
6-5
BOX PLOTS
6-6
TIME SEQUENCE PLOTS
6-7
PROBABILITY PLOTS
6-8
MORE ABOUT PROBABILITY PLOTTING (CD ONLY)
7-2
GENERAL CONCEPTS OF POINT ESTIMATION
7-3
METHODS OF POINT ESTIMATION
7-5
SAMPLING DISTRIBUTIONS OF MEANS
8-2
CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
8-3
CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE UNKNOWN
8-4
CONFIDENCE INTERVAL ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION
8-5
A LARGE-SAMPLE CONFIDENCE INTERVAL FOR A POPULATION PROPORTION
8-6
A PREDICTION INTERVAL FOR A FUTURE OBSERVATION
8-7
TOLERANCE INTERVALS FOR A NORMAL DISTRIBUTION
9-1
HYPOTHESIS TESTING
9-2
TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
9-3
TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE UNKNOWN
9-4
HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION
9-5
TESTS ON A POPULATION PROPORTION
9-7
TESTING FOR GOODNESS OF FIT
10-3
INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN
10-4
INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN
10-5
INFERENCES ON THE VARIANCES OF TWO NORMAL POPULATIONS
10-6
INFERENCE ON TWO POPULATION PROPORTIONS
10-7
SUMMARY TABLE FOR INFERENCE PROCEDURES FOR TWO SAMPLES
10.2
INFERENCE FOR A DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES KNOWN
11-11
CORRELATION
11-2
SIMPLE LINEAR REGRESSION
11-5
HYPOTHESIS TESTS IN SIMPLE LINEAR REGRESSION
11-7
PREDICTION OF NEW OBSERVATIONS
11-8
ADEQUACY OF THE REGRESSION MODEL
12-1
MULTIPLE LINEAR REGRESSION MODEL
12-2
MULTIPLE LINEAR REGRESSION MODEL
12-3
CONFIDENCE INTERVALS IN MULTIPLE LINEAR REGRESSION
12-5
MODEL ADEQUACY CHECKING
12-6
ASPECTS OF MULTIPLE REGRESSION MODELING
13-2
THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT
13-4
RANDOMIZED COMPLETE BLOCK DESIGN
14-4
TWO-FACTOR FACTORIAL EXPERIMENTS
14-5
GENERAL FACTORIAL EXPERIMENTS
14-7
2k FACTORIAL DESIGNS
14-8
BLOCKING AND CONFOUNDING IN THE 2k DESIGN
14-9
FRACTIONAL REPLICATION OF THE 2k DESIGN
15-2
SIGN TEST
15-3
WILCOXON SIGNED-RANK TEST
15-4
WILCOXON RANK-SUM TEST
15-5
NONPARAMETRIC METHODS IN THE ANALYSIS OF VARIANCE
16-10
CUMULATIVE SUM CONTROL CHART
16-12
IMPLEMENTING SPC
16-5
x AND R OR S CONTROL CHARTS
16-6
CONTROL CHARTS FOR INDIVIDUAL MEASUREMENTS
16-7
PROCESS CAPABILITY
16-8
ATTRIBUTE CONTROL CHARTS
16-9
CONTROL CHART PERFORMANCE
33-3
THE RANDOM-EFFECTS MODEL
Textbook Solutions for Applied Statistics and Probability for Engineers
Chapter 5-3 Problem 5-41
Question
Continuation of Exercise 5-40. Determine the following:
Solution
The first step in solving 5-3 problem number 8 trying to solve the problem we have to refer to the textbook question: Continuation of Exercise 5-40. Determine the following:
From the textbook chapter TWO CONTINUOUS RANDOM VARIABLES you will find a few key concepts needed to solve this.
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full solution
full solution
Title
Applied Statistics and Probability for Engineers 3
Author
Douglas C. Montgomery, George C. Runger
ISBN
9780471204541
Continuation of Exercise 5-40. Determine the following
Chapter 5-3 textbook questions
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
5-35. Continuation of Exercise 5-34. Determine the following: (a) (b) (c) (d) (e) E(X) (f) P1X 0, Y 42 P11 Y 2.52 P1X 1.8, 1 Y 2.52 P1X 2, Y 32 P1X 2.52
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-34. Determine the following: (a) Marginal probability distribution of the random variable X (b) Conditional probability distribution of Y given that X 1.5 (c) (d) (e) Conditional probability distribution of X given that Y 2
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
5-37. 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 x y x 2.
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-37. Determine the following: (a) (b) (c) (d) (e) E(X)
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
5-39. Continuation of Exercise 5-37. Determine the following: (a) Marginal probability distribution of X (b) Conditional probability distribution of Y given that X 1 (c) (d) (e) Conditional probability distribution of X given that Y 2
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Determine the value of c that makes the function f(x, y) cxy a joint probability density function over the range 0 x 3 and 0 y x
Read more -
Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-40. Determine the following:
Read more -
Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-40. Determine the following: (a) Marginal probability distribution of X (b) Conditional probability distribution of Y given X 1 (c) (d) (e) Conditional probability distribution of X given Y 2
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Determine the value of c that makes the function a joint probability density function over the range 0 x and 0 y x
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-43. Determine the following: (a) (b) (c) (d) (e) E(X) (f) E(Y)
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
5-45. Continuation of Exercise 5-43. Determine the following: (a) Marginal probability distribution of X (b) Conditional probability distribution of Y given X 1 (c) (d) Conditional probability distribution of X given Y 2
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Determine the value of c that makes the function a joint probability density function over the range 0 x and x y
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-46. Determine the following:
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-46. Determine the following: (a) Marginal probability distribution of X (b) Conditional probability distribution of Y given X 1 (c) (d) (e) Conditional probability distribution of X given Y 2
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
5-49. 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 1 y x 1. That is, fXY (x, y) c for x and y in the region. Determine the value for c such that fXY (x, y) is a joint probability density function.
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
Continuation of Exercise 5-49. Determine the following:
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
5-51. Continuation of Exercise 5-49. Determine the following: (a) Marginal probability distribution of X (b) Conditional probability distribution of Y given X 1
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
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 40 hours of operation? (b) What is the probability that all three lines experience a surface finish problem between 20 and 40 hours of operation? (c) Why is the joint probability density function not needed to answer the previous questions?
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
5-53. 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 orders will be received in a 5 minute period? In a 10 minute period? (b) What is the probability that both systems receive two orders between 10 and 15 minutes after the site is offi- cially open for business?
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Chapter 5: Problem 5 Applied Statistics and Probability for Engineers 3
The conditional probability distribution of Y given X x is for y 0 and the marginal probability distribution of X is a continuous uniform distribution over 0 to 10. (a) Graph for y 0 for several values of x. Determine (b) (c) (d) (e) (f) fY 1 y2 fXY E1Y X x2 1x, y2 P1Y 2 X 22 E1Y X 22
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