Excursions in Modern Mathematics, Books a la carte edition (9th Edition)
9th Edition
ISBN: 9780134469041
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 17, Problem 10E
Estimate the value of the standard deviation
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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
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(Yi — mi)²
σ
2
By minimising oc², derive the formulae
for the best values of the model for
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126 1/2"
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Chapter 17 Solutions
Excursions in Modern Mathematics, Books a la carte edition (9th Edition)
Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider a normal distribution with mean =81.2lb...Ch. 17 - Consider a normal distribution with mean =2354...Ch. 17 - Consider a normal distribution with first quartile...Ch. 17 - Consider a normal distribution with first quartile...Ch. 17 - Estimate the value of the standard deviation ...Ch. 17 - Estimate the value of the standard deviation ...
Ch. 17 - Explain why a distribution with median M=82, mean...Ch. 17 - Explain why a distribution with median M=453, mean...Ch. 17 - Explain why a distribution with =195, Q1=180 and...Ch. 17 - Explain why a distribution with M==47, Q1=35 and...Ch. 17 - A normal distribution has mean =30kg and standard...Ch. 17 - Prob. 16ECh. 17 - Prob. 17ECh. 17 - Prob. 18ECh. 17 - Prob. 19ECh. 17 - In a normal distribution with mean =83.2 and...Ch. 17 - Prob. 21ECh. 17 - Prob. 22ECh. 17 - Prob. 23ECh. 17 - Prob. 24ECh. 17 - Prob. 25ECh. 17 - In a normal distribution with standard deviation...Ch. 17 - Prob. 27ECh. 17 - Prob. 28ECh. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution defined by Fig....Ch. 17 - Consider the normal distribution defined by Fig....Ch. 17 - A normal distribution has mean =71.5in., and the...Ch. 17 - A normal distribution has standard deviation =12.3...Ch. 17 - Prob. 35ECh. 17 - Prob. 36ECh. 17 - Prob. 37ECh. 17 - A normal distribution has mean =500 and standard...Ch. 17 - In a normal distribution, what percent of the data...Ch. 17 - In a normal distribution, what percent of the data...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - An honest coin is tossed n=3600 times. Let the...Ch. 17 - Prob. 58ECh. 17 - Suppose that a random sample of n=7056 adults is...Ch. 17 - An honest die is rolled. If the roll comes out...Ch. 17 - A dishonest coin with probability of heads p=0.4...Ch. 17 - A dishonest coin with probability of heads p=0.75...Ch. 17 - Prob. 63ECh. 17 - Suppose that 1 out of every 10 plasma televisions...Ch. 17 - Prob. 65ECh. 17 - Prob. 66ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 68ECh. 17 - Prob. 69ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 71ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 73ECh. 17 - Prob. 74ECh. 17 - Prob. 75ECh. 17 - Prob. 76ECh. 17 - A dishonest coin with probability of heads p=0.1...Ch. 17 - Prob. 78ECh. 17 - In American roulette there are 18 red numbers, 18...Ch. 17 - After polling a random sample of 800 voters during...
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