- 5.5.1: Let X be a random variable with probability densityfunction (a) Wha...
- 5.5.2: A system consisting of one original unit plus aspare can function f...
- 5.5.3: Consider the functionf (x) =0C(2x x3) 0 < x < 520 otherwiseCould f ...
- 5.5.4: The probability density function of X, the lifetimeof a certain typ...
- 5.5.5: A filling station is supplied with gasoline once aweek. If its week...
- 5.5.6: Compute E[X] if X has a density function given by
- 5.5.7: The density function of X is given by If E[X] = 35, find a and b.
- 5.5.8: The lifetime in hours of an electronic tube is a randomvariable hav...
- 5.5.9: Consider Example 4b of Chapter 4, but now supposethat the seasonal ...
- 5.5.10: Trains headed for destination A arrive at the trainstation at 15-mi...
- 5.5.11: A point is chosen at random on a line segmentof length L. Interpret...
- 5.5.12: A bus travels between the two cities A and B,which are 100 miles ap...
- 5.5.13: You arrive at a bus stop at 10 oclock, knowingthat the bus will arr...
- 5.5.14: Let X be a uniform (0, 1) random variable. ComputeE[Xn] by using Pr...
- 5.5.15: If X is a normal random variable with parameters = 10 and 2 = 36, c...
- 5.5.16: The annual rainfall (in inches) in a certain region isnormally dist...
- 5.5.17: A man aiming at a target receives 10 points if hisshot is within 1 ...
- 5.5.18: Suppose that X is a normal random variable withmean 5. If P{X > 9} ...
- 5.5.19: Let X be a normal random variable with mean12 and variance 4. Find ...
- 5.5.20: If 65 percent of the population of a large communityis in favor of ...
- 5.5.21: Suppose that the height, in inches, of a 25-year-oldman is a normal...
- 5.5.22: The width of a slot of a duralumin forging is (ininches) normally d...
- 5.5.23: One thousand independent rolls of a fair die willbe made. Compute a...
- 5.5.24: The lifetimes of interactive computer chips producedby a certain se...
- 5.5.25: Each item produced by a certain manufacturer is,independently, of a...
- 5.5.26: Two types of coins are produced at a factory: a faircoin and a bias...
- 5.5.27: In 10,000 independent tosses of a coin, the coinlanded on heads 580...
- 5.5.28: Twelve percent of the population is left handed.Approximate the pro...
- 5.5.29: A model for the movement of a stock supposesthat if the present pri...
- 5.5.30: An image is partitioned into two regions, onewhite and the other bl...
- 5.5.31: (a) A fire station is to be located along a road oflength A,A < q. ...
- 5.5.32: The time (in hours) required to repair a machine isan exponentially...
- 5.5.33: The number of years a radio functions is exponentiallydistributed w...
- 5.5.34: Jones figures that the total number of thousandsof miles that an au...
- 5.5.35: The lung cancer hazard rate (t) of a t-year-oldmale smoker is such ...
- 5.5.36: Suppose that the life distribution of an item has thehazard rate fu...
- 5.5.37: If X is uniformly distributed over (1, 1), find(a) P{|X| > 12};(b) ...
- 5.5.38: If Y is uniformly distributed over (0, 5), whatis the probability t...
- 5.5.39: If X is an exponential random variable withparameter = 1, compute t...
- 5.5.40: If X is uniformly distributed over (0, 1), find thedensity function...
- 5.5.41: Find the distribution of R = Asin , where A isa fixed constant and ...
Solutions for Chapter 5: Continuous Random Variables
Full solutions for First Course in Probability | 8th Edition
ISBN: 9780136033134
Summary of Chapter 5: Continuous Random Variables
Since 41 problems in chapter 5: Continuous Random Variables have been answered, more than 26609 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: First Course in Probability, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. First Course in Probability was written by and is associated to the ISBN: 9780136033134. Chapter 5: Continuous Random Variables includes 41 full step-by-step solutions.
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All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
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Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
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Analytic study
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
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Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
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Cause-and-effect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
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Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
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Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
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Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
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Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
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Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
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Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
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Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
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Discrete random variable
A random variable with a inite (or countably ininite) range.
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Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
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Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
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Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
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Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .