 3.11.1: Suppose that X and Y are independent random variables, that X has t...
 3.11.2: Suppose that X and Y are independent random variables. Suppose that...
 3.11.3: Suppose that the random variable X has the following c.d.f.: F (x) ...
 3.11.4: Suppose that the random variable X has a continuous distribution wi...
 3.11.5: Suppose that X1 and X2 are i.i.d. random variables, and that each h...
 3.11.6: For each value of p > 1, let c(p) = x=1 1 xp . Suppose that the ran...
 3.11.7: Suppose that X1 and X2 are i.i.d. random variables, each of which h...
 3.11.8: Suppose that an electronic system comprises four components, and le...
 3.11.9: Suppose that a box contains a large number of tacks and that the pr...
 3.11.10: Suppose that the radius X of a circle is a random variable having t...
 3.11.11: Suppose that the random variable X has the following p.d.f.: f (x) ...
 3.11.12: Suppose that the 12 random variables X1,...,X12 are i.i.d. and each...
 3.11.13: Suppose that the joint distribution of X and Y is uniform over a se...
 3.11.14: Suppose that X and Y are independent random variables with the foll...
 3.11.15: Suppose that, on a particular day, two persons A and B arrive at a ...
 3.11.16: Suppose that X and Y have the following joint p.d.f.: f (x, y) = 2(...
 3.11.17: Suppose that X and Y are random variables. The marginal p.d.f. of X...
 3.11.18: Suppose that the joint distribution of X and Y is uniform over the ...
 3.11.19: Suppose that the random variables X, Y , and Z have the following j...
 3.11.20: Suppose that the random variables X, Y , and Z have the following j...
 3.11.21: Suppose that X and Y are i.i.d. random variables, and that each has...
 3.11.22: Suppose that the random variables X and Y have the following joint ...
 3.11.23: Suppose that X1,...,Xn are i.i.d. random variables, each having the...
 3.11.24: Suppose that X1, X2, and X3 form a random sample of three observati...
 3.11.25: In this exercise, we shall provide an approximate justification for...
 3.11.26: Let X1, X2 be two independent random variables each with p.d.f. f1(...
 3.11.27: Three boys A, B, and C are playing table tennis. In each game, two ...
 3.11.28: Consider again the Markov chain described in Exercise 27. (a) Deter...
 3.11.29: Find the unique stationary distribution for theMarkov chain in Exer...
Solutions for Chapter 3.11: Random Variables and Distributions
Full solutions for Probability and Statistics  4th Edition
ISBN: 9780321500465
Solutions for Chapter 3.11: Random Variables and Distributions
Get Full SolutionsChapter 3.11: Random Variables and Distributions includes 29 full stepbystep solutions. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. This expansive textbook survival guide covers the following chapters and their solutions. Since 29 problems in chapter 3.11: Random Variables and Distributions have been answered, more than 16585 students have viewed full stepbystep solutions from this chapter.

Arithmetic mean
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Crossed factors
Another name for factors that are arranged in a factorial experiment.

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

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.

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.

Error variance
The variance of an error term or component in a model.

Exhaustive
A property of a collection of events that indicates that their union equals the sample space.

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.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.