 8.1: The following table gives the observed counts in 1second intervals...
 8.2: The Poisson distribution has been used by traffic engineers as a mo...
 8.3: One of the earliest applications of the Poisson distribution was ma...
 8.4: Suppose that X is a discrete random variable with P(X = 0) = 2 3 P(...
 8.5: Suppose that X is a discrete random variable with P(X = 1) = and P(...
 8.6: Suppose that X bin(n, p). a. Show that the mle of p is p = X/n. b. ...
 8.7: Suppose that X follows a geometric distribution, P(X = k) = p(1 p)k...
 8.8: In an ecological study of the feeding behavior of birds, the number...
 8.9: How would you respond to the following argument? This talk of sampl...
 8.10: Use the normal approximation of the Poisson distribution to sketch ...
 8.11: In ExampleAof Section 8.4, we used knowledge of the exact form of t...
 8.12: Suppose that you had to choose either the method of moments estimat...
 8.13: In Example D of Section 8.4, the method of moments estimate was fou...
 8.14: In Example C of Section 8.5, how could you use the bootstrap to est...
 8.15: The upper quartile of a distribution with cumulative distribution F...
 8.16: Consider an i.i.d. sample of random variables with density function...
 8.17: Suppose that X1, X2, . . . , Xn are i.i.d. random variables on the ...
 8.18: Suppose that X1, X2, . . . , Xn are i.i.d. random variables on the ...
 8.19: Suppose that X1, X2, . . . , Xn are i.i.d. N(, 2). a. If is known, ...
 8.20: Suppose that X1, X2, . . . , X25 are i.i.d. N(, 2), where = 0 and =...
 8.21: Suppose that X1, X2, . . . , Xn are i.i.d. with density function f ...
 8.22: TheWeibull distributionwas defined in of Chapter 2. This distributi...
 8.23: A company has manufactured certain objects and has printed a serial...
 8.24: Find a very new shiny penny. Hold it on its edge and spin it. Do th...
 8.25: If a thumbtack is tossed in the air, it can come to rest on the gro...
 8.26: In an effort to determine the size of an animal population, 100 ani...
 8.27: Suppose that certain electronic components have lifetimes that are ...
 8.28: Why do the intervals in the left panel of Figure 8.8 have different...
 8.29: Are the estimates of 2 at the centers of the confidence intervals s...
 8.30: The exponential distribution is f (x; ) = ex and E(X) = 1. The cumu...
 8.31: George spins a coin three times and observes no heads. He then give...
 8.32: The following 16 numbers came from normal random number generator o...
 8.33: Suppose that X1, X2, . . . , Xn are i.i.d. N(, 2), where and are un...
 8.34: Suppose that X1, X2, . . . , Xn are i.i.d. N(0, 2 0 ) and and 2 are...
 8.35: (Bootstrap in Example A of Section 8.5.1) Let U1,U2, . . . ,U1029 b...
 8.36: How do the approximate 90% confidence intervals in Example E of Sec...
 8.37: Using the notation of Section 8.5.3, suppose that and are lower and...
 8.38: Continuing 37, show that if the sampling distribution of is symmetr...
 8.39: In Section 8.5.3, the bootstrap confidence intervalwas derived from...
 8.40: In Example A of Section 8.5.1, how could you use the bootstrap to e...
 8.41: What are the relative efficiencies of the method of moments and max...
 8.42: The file gammaray contains a small quantity of data collected from...
 8.43: The file gammaarrivals contains another set of gammaray data, thi...
 8.44: The file bodytemp contains normal body temperature readings (degree...
 8.45: A Random Walk Model for Chromatin. A human chromosome is a very lar...
 8.46: The data of this exercise were gathered as part of a study to estim...
 8.47: The Pareto distribution has been used in economics as a model for a...
 8.48: Consider the following method of estimating for a Poisson distribut...
 8.49: For the example on muon decay in Section 8.4, suppose that instead ...
 8.50: Let X1, . . . , Xn be an i.i.d. sample from a Rayleigh distribution...
 8.51: The double exponential distribution is f (x) = 1 2 ex , < x < Fo...
 8.52: Let X1, . . . , Xn be i.i.d. random variables with the density func...
 8.53: Let X1, . . . , Xn be i.i.d. uniform on [0, ]. a. Find the method o...
 8.54: Suppose that an i.i.d. sample of size 15 from a normal distribution...
 8.55: For two factorsstarchy or sugary, and green base leaf or white base...
 8.56: Referring to 55, consider two other estimates of . (1) The expected...
 8.57: This problem is concerned with the estimation of the variance of a ...
 8.58: If gene frequencies are in equilibrium, the genotypes AA, Aa, and a...
 8.59: Suppose that in the population of twins, males (M) and females (F) ...
 8.60: Let X1, . . . , Xn be an i.i.d. sample from an exponential distribu...
 8.61: Laplaces rule of succession. Laplace claimed that when an event hap...
 8.62: Show that the gamma distribution is a conjugate prior for the expon...
 8.63: Suppose that 100 items are sampled from a manufacturing process and...
 8.64: This is a continuation of the previous problem. Let X = 0 or 1 acco...
 8.65: Suppose that a random sample of size 20 is taken from a normal dist...
 8.66: Let the unknown probability that a basketball player makes a shot s...
 8.67: Evans (1953) considered fitting the negative binomial distribution ...
 8.68: Let X1, . . . , Xn be an i.i.d. sample from a Poisson distribution ...
 8.69: Use the factorization theorem (Theorem A in Section 8.8.1) to concl...
 8.70: Use the factorization theorem to find a sufficient statistic for th...
 8.71: Let X1, . . . , Xn be an i.i.d. sample from a distribution with the...
 8.72: Show that 3n i=1 Xi and n i=1 Xi are sufficient statistics for the ...
 8.73: Find a sufficient statistic for the Rayleigh density, f (x) = x 2 ...
 8.74: Show that the binomial distribution belongs to the exponential family.
 8.75: Show that the gamma distribution belongs to the exponential family.
Solutions for Chapter 8: Estimation of Parameters and Fitting of Probability Distributions
Full solutions for Mathematical Statistics and Data Analysis  3rd Edition
ISBN: 9788131519547
Solutions for Chapter 8: Estimation of Parameters and Fitting of Probability Distributions
Get Full SolutionsSince 75 problems in chapter 8: Estimation of Parameters and Fitting of Probability Distributions have been answered, more than 15395 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 8: Estimation of Parameters and Fitting of Probability Distributions includes 75 full stepbystep solutions. Mathematical Statistics and Data Analysis was written by and is associated to the ISBN: 9788131519547. This textbook survival guide was created for the textbook: Mathematical Statistics and Data Analysis, edition: 3.

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

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

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.

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

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.

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

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.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

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 normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Defectsperunit control chart
See U chart

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Estimate (or point estimate)
The numerical value of a point estimator.

Frequency distribution
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

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.