 5.1: Let X1, X2, . . . be a sequence of independent random variables wit...
 5.2: Let Xi be as in but with E(Xi ) = i and n1n i=1 i . Show that X in ...
 5.3: Suppose that the number of insurance claims, N, filed in a year is ...
 5.4: Suppose that the number of traffic accidents, N, in a given period ...
 5.5: Using momentgenerating functions, show that as n , p 0, and np , t...
 5.6: Using momentgenerating functions, show that as the gamma distribut...
 5.7: Show that if Xn c in probability and if g is a continuous function,...
 5.8: Compare the Poisson cdf and the normal approximation for (a) = 10, ...
 5.9: Compare the binomial cdf and the normal approximation for (a) n = 2...
 5.10: A sixsided die is rolled 100 times. Using the normal approximation...
 5.11: A skeptic gives the following argument to show that there must be a...
 5.12: The central limit theorem can be used to analyze roundoff error. S...
 5.13: A drunkard executes a random walk in the following way: Each minute...
 5.14: Answer under the assumption that the drunkard has some idea of wher...
 5.15: Suppose that you bet $5 on each of a sequence of 50 independent fai...
 5.16: Suppose that X1, . . . , X20 are independent random variables with ...
 5.17: Suppose that a measurement has mean and variance 2 = 25. Let X be t...
 5.18: Suppose that a company ships packages that are variable in weight, ...
 5.19: a. U se the Monte Carlo method with n = 100 and n = 1000 to estimat...
 5.20: What is the variance of the estimate of an integral by the Monte Ca...
 5.21: This problem introduces a variation on the Monte Carlo integration ...
 5.22: Use the central limit theorem to find _ such that P( I ( f ) I ( f...
 5.23: An irregularly shaped object of unknown area A is located in the un...
 5.24: How could the central limit theorem be used to gauge the probable s...
 5.25: Let X be a continuous random variable with density function f (x) =...
 5.26: Suppose that a basketball player can score on a particular shot wit...
 5.27: Prove that if an a, then (1 + an/n)n ea.
 5.28: Let fn be a sequence of frequency functions with fn(x) = 1 2 if x =...
 5.29: In addition to limit theorems that deal with sums, there are limit ...
 5.30: Generate a sequence U1,U2, . . . ,U1000 of independent uniform rand...
Solutions for Chapter 5: Limit Theorems
Full solutions for Mathematical Statistics and Data Analysis  3rd Edition
ISBN: 9788131519547
Solutions for Chapter 5: Limit Theorems
Get Full SolutionsSince 30 problems in chapter 5: Limit Theorems have been answered, more than 15219 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Mathematical Statistics and Data Analysis, edition: 3. Mathematical Statistics and Data Analysis was written by and is associated to the ISBN: 9788131519547. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5: Limit Theorems includes 30 full stepbystep solutions.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

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.

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

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.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Coeficient of determination
See R 2 .

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.

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

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.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Error mean square
The error sum of squares divided by its number of degrees of freedom.

Experiment
A series of tests in which changes are made to the system under study

Exponential random variable
A series of tests in which changes are made to the system under study

Factorial experiment
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

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