Excursions in Modern Mathematics (9th Edition)
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 14, Problem 8E

To estimate the population in a rookery, 4965 fur seal pups were captured and tagged in early August. In late August, 900 fur seal pups were captured. Of these, 218 had been tagged. Based on these figures, estimate the population of fur seal pups in the rookery. [Source: Chapman and Johnson, “Estimation of Fur Seal Pup Populations by Randomized Sampling,” Transactions of the America Fisheries Society, 97 (July 1968), 264-270.]

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Module Code: MATH380202 1. (a) Define the terms "strongly stationary" and "weakly stationary". Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is weakly stationary, define the autocorrelation function (acf) Pk, for lag k. What conditions must a process {X+) satisfy for it to be white noise? (b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of the following processes {X+} are weakly stationary for t> 0? Briefly justify your answers. i. Xt for all > 0. ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0. (c) Provide an expression for estimating the autocovariance function for a sample X1,..., X believed to be from a weakly stationary process. How is the autocor- relation function Pk then estimated, and a correlogram (or acf plot) constructed? (d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where {E} is a white noise process with variance 1. Compute the population autocorre- lation function Pk for all k = 0, 1, ....
iii) i=5 x² = Σ i=1 (Yi — mi)² σ 2 By minimising oc², derive the formulae for the best values of the model for a 1 degree polynomial (2 parameters).
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Chapter 14 Solutions

Excursions in Modern Mathematics (9th Edition)

Ch. 14 - Exercises 11 and 12 refer to Chapmans correction....Ch. 14 - Exercises 11 and 12 refer to Chapmans correction....Ch. 14 - Starting in 2004, a study to determine the number...Ch. 14 - Exercises 25 through 28 refer to the following...Ch. 14 - Name the sampling method that best describes each...Ch. 14 - An audit is performed on last years 15, 000...Ch. 14 - Exercise17 through 20 refer to the following...Ch. 14 - Exercise17 through 20 refer to the following...Ch. 14 - Exercise17 through 20 refer to the following...Ch. 14 - Exercise17 through 20 refer to the following...Ch. 14 - Prob. 21ECh. 14 - Prob. 22ECh. 14 - Prob. 23ECh. 14 - Prob. 24ECh. 14 - Exercises 25 through 28 refer to the following...Ch. 14 - Exercises 25 through 28 refer to the following...Ch. 14 - Exercises 25 through 28 refer to the following...Ch. 14 - Exercises 29 and 30 refer to the following story:...Ch. 14 - Exercises 29 and 30 refer to the following story:...Ch. 14 - Prob. 31ECh. 14 - Prob. 32ECh. 14 - Exercises 33 through 36 refer to the following...Ch. 14 - Exercises 33 through 36 refer to the following...Ch. 14 - Exercises 33 through 36 refer to the following...Ch. 14 - Exercises 33 through 36 refer to the following...Ch. 14 - Exercises 37 through 40 refer to a clinical study...Ch. 14 - Exercises 37 through 40 refer to a clinical study...Ch. 14 - Exercises 37 through 40 refer to a clinical study...Ch. 14 - Prob. 40ECh. 14 - Prob. 41ECh. 14 - Exercises 41 through 44 refer to a clinical trial...Ch. 14 - Prob. 43ECh. 14 - Exercises 41 through 44 refer to a clinical trial...Ch. 14 - Prob. 45ECh. 14 - Prob. 46ECh. 14 - Exercises 45 through 48 refer to a study on the...Ch. 14 - Prob. 48ECh. 14 - Exercises 49 through 52 refer to a landmark study...Ch. 14 - Prob. 50ECh. 14 - Exercises 49 through 52 refer to a landmark study...Ch. 14 - Prob. 52ECh. 14 - Exercises 53 through 56 refer to a study conducted...Ch. 14 - Prob. 54ECh. 14 - Exercises53_ through 56_ refer to a study...Ch. 14 - Exercises53 through 56 refer to a study conducted...Ch. 14 - Prob. 57ECh. 14 - Prob. 58ECh. 14 - Exercises 57 through 60 refer to the following...Ch. 14 - Prob. 60ECh. 14 - Prob. 61ECh. 14 - Prob. 62ECh. 14 - Prob. 63ECh. 14 - Prob. 64ECh. 14 - Read the examples of informal surveys given in...Ch. 14 - Leading-question bias. The way the questions in...Ch. 14 - Prob. 67ECh. 14 - Prob. 68ECh. 14 - Prob. 69ECh. 14 - Prob. 70ECh. 14 - Prob. 71ECh. 14 - Prob. 72ECh. 14 - One of the problems with the capture-recapture...Ch. 14 - Darrochs method. is a method for estimating the...
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