Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Textbook Question
Chapter 7.B, Problem 1QQ
The probability of rolling two dice and getting a double−1 (making a sum of 2, or “snake eyes”) is 1 in 36. Suppose you roll two dice twice. Which statement is not true?
a. The probability of getting a double -1 is 1/36 for each individual roll.
b. The probability of getting a double -1 both times is .
c. The probability of getting a double -1 on at least one of the two rolls is .
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Students have asked these similar questions
Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
AR and MA orders of this representation.
(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.
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, ....
Chapter 7 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. 7.A - Suppose you toss one coin three times in a row and...Ch. 7.A - During the course of the basketball season, Shawna...Ch. 7.A - A box contains 20 chocolates, but only 2 of them...Ch. 7.A - Prob. 4QQCh. 7.A - When you toss one coin, the probability that...Ch. 7.A - On a roll of two dice, Serena bets that the sum...Ch. 7.A - Suppose you toss four 6-sided dice. How many...Ch. 7.A - Suppose you toss four 6-sided dice. How many...Ch. 7.A - You are playing 5-card poker with a deck of 52...Ch. 7.A - Prob. 10QQ
Ch. 7.A - Distinguish between an outcome and an event in...Ch. 7.A - 2. What does it mean when we write P(event)? What...Ch. 7.A - Briefly describe the differences among...Ch. 7.A - How is the probability of an event not occurring...Ch. 7.A - Prob. 5ECh. 7.A - Prob. 6ECh. 7.A - When I toss four coins, there are four different...Ch. 7.A - The probability that my sister will get into the...Ch. 7.A - I estimate that the probability of my getting...Ch. 7.A - Because either there is life on Mars or there is...Ch. 7.A - The probability that Jonas will win the race is...Ch. 7.A - Based on data showing that we’ve had snow on...Ch. 7.A - Prob. 13ECh. 7.A - 13-16: Review of the Multiplication Principle. Use...Ch. 7.A - Review of the Multiplication Principle. Use the...Ch. 7.A - Prob. 16ECh. 7.A - Prob. 17ECh. 7.A - Double-Header Outcomes and Events. Suppose the New...Ch. 7.A - Prob. 19ECh. 7.A - Prob. 20ECh. 7.A - Prob. 21ECh. 7.A - Prob. 22ECh. 7.A - Prob. 23ECh. 7.A - Prob. 24ECh. 7.A - 19-28: Theoretical Probabilities. Use the...Ch. 7.A - Theoretical Probabilities. Use the theoretical...Ch. 7.A - 19-28: Theoretical Probabilities. Use the...Ch. 7.A - 19-28: Theoretical Probabilities. Use the...Ch. 7.A - Prob. 29ECh. 7.A - Prob. 30ECh. 7.A - Prob. 31ECh. 7.A - Prob. 32ECh. 7.A - Which Type of Probability? State which method...Ch. 7.A - 33-34: Which Type of Probability? State which...Ch. 7.A - Prob. 35ECh. 7.A - Prob. 36ECh. 7.A - Event Not Occurring. Determine the probability of...Ch. 7.A - Prob. 38ECh. 7.A - Probability Distributions. Make a probability...Ch. 7.A - 39-42: Probability Distributions. Make a...Ch. 7.A - 39-42: Probability Distributions. Make a...Ch. 7.A - 39-42: Probability Distributions. Make a...Ch. 7.A - Prob. 43ECh. 7.A - Prob. 44ECh. 7.A - Prob. 45ECh. 7.A - Prob. 46ECh. 7.A - Prob. 47ECh. 7.A - Prob. 48ECh. 7.A - Prob. 49ECh. 7.A - Prob. 50ECh. 7.A - Prob. 51ECh. 7.A - Prob. 52ECh. 7.A - Prob. 53ECh. 7.A - Prob. 54ECh. 7.A - Computing Probabilities. Decide which method...Ch. 7.A - Computing Probabilities. Decide which method...Ch. 7.A - Prob. 57ECh. 7.A - Prob. 58ECh. 7.A - Prob. 59ECh. 7.A - Computing Probabilities. Decide which method...Ch. 7.A - Prob. 61ECh. 7.A - Prob. 62ECh. 7.A - Prob. 63ECh. 7.A - Prob. 64ECh. 7.A - Prob. 65ECh. 7.A - Prob. 66ECh. 7.A - Prob. 67ECh. 7.A - Probability Distributions 68.Suppose you have a...Ch. 7.A - Prob. 69ECh. 7.A - More Counting. Answer the following counting...Ch. 7.A - Prob. 71ECh. 7.A - Prob. 72ECh. 7.A - Prob. 73ECh. 7.A - Prob. 74ECh. 7.A - Senior Citizens. In 2010, there were 40 million...Ch. 7.A - Prob. 76ECh. 7.A - Prob. 77ECh. 7.A - Prob. 78ECh. 7.A - Prob. 79ECh. 7.A - Prob. 80ECh. 7.A - Prob. 81ECh. 7.A - Probability in the News. Find a news article or...Ch. 7.A - Prob. 83ECh. 7.A - Gambling Odds. Find an advertising for a gambling...Ch. 7.B - The probability of rolling two dice and getting a...Ch. 7.B - The rule PAandB=PAPBholdsa. in all cases.b. only...Ch. 7.B - Prob. 3QQCh. 7.B - A box of candy contains five dark chocolates and...Ch. 7.B - Prob. 5QQCh. 7.B - You roll two dice. Based on the probabilities...Ch. 7.B - You roll two dice twice. Based on the...Ch. 7.B - You toss two coins ten times, and you want to know...Ch. 7.B - Prob. 9QQCh. 7.B - Prob. 10QQCh. 7.B - How did the gambling habits of the Chevalier de...Ch. 7.B - 2. Give an example in which we would be interested...Ch. 7.B - 3. Give an example in which we would be interested...Ch. 7.B - 4. What is the at least once rule? Explain how the...Ch. 7.B - The probability of getting heads and tails when...Ch. 7.B - If you toss a corn and get heads three times in a...Ch. 7.B - The probability of drawing ace or a spade from a...Ch. 7.B - I can’t believe you chose the lottery number...Ch. 7.B - Prob. 9ECh. 7.B - To find the probability that at least one of my 25...Ch. 7.B - Chevalier’s Logic with Coins. The Chevalier’s...Ch. 7.B - Prob. 12ECh. 7.B - Prob. 13ECh. 7.B - Prob. 14ECh. 7.B - Prob. 15ECh. 7.B - Prob. 16ECh. 7.B - Prob. 17ECh. 7.B - Prob. 18ECh. 7.B - Prob. 19ECh. 7.B - Prob. 20ECh. 7.B - Prob. 21ECh. 7.B - Prob. 22ECh. 7.B - Prob. 23ECh. 7.B - 2 1-24: Either/Or Probabilities. Determine whether...Ch. 7.B - Prob. 25ECh. 7.B - 26. Randomly meeting three international students...Ch. 7.B - Prob. 27ECh. 7.B - Prob. 28ECh. 7.B - Prob. 29ECh. 7.B - Prob. 30ECh. 7.B - At Least Once Problems. Use the at least once rule...Ch. 7.B - Prob. 32ECh. 7.B - Prob. 33ECh. 7.B - Prob. 34ECh. 7.B - Prob. 35ECh. 7.B - Prob. 36ECh. 7.B - Prob. 37ECh. 7.B - Prob. 38ECh. 7.B - Prob. 39ECh. 7.B - Prob. 40ECh. 7.B - Prob. 41ECh. 7.B - Prob. 42ECh. 7.B - Prob. 43ECh. 7.B - Prob. 44ECh. 7.B - Prob. 45ECh. 7.B - Prob. 46ECh. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Prob. 49ECh. 7.B - Prob. 50ECh. 7.B - Prob. 51ECh. 7.B - Prob. 52ECh. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Prob. 54ECh. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Assorted Probabilities. Use the method of your...Ch. 7.B - Probability and Court. The data in the following...Ch. 7.B - Testing a Drug. A new cold medication was tested...Ch. 7.B - Prob. 59ECh. 7.B - Dominant and Recessive Genes. Many traits are...Ch. 7.B - Better Bet for the Chevalier. Suppose that the...Ch. 7.B - Prob. 62ECh. 7.B - Miami Hurricanes. Studies of the Florida...Ch. 7.B - Prob. 64ECh. 7.B - Prob. 65ECh. 7.B - Prob. 66ECh. 7.B - Prob. 67ECh. 7.B - Combined Probability in Your Life. Cite a recent...Ch. 7.C - Suppose that the probability of a hurricane...Ch. 7.C - Consider a lottery with 100 million tickets in...Ch. 7.C - Consider the lottery described in Exercise 2. If...Ch. 7.C - Prob. 4QQCh. 7.C - An insurance company knows that the average cost...Ch. 7.C - You know a shortcut to work that uses side streets...Ch. 7.C - Cameron is betting on a game in which the...Ch. 7.C - Prob. 8QQCh. 7.C - A $1 slot at a casino is set so that it returns...Ch. 7.C - Consider the slot machine described in Exercise 9....Ch. 7.C - Explain the meaning of the law of large numbers....Ch. 7.C - In 10 tosses of a fair coin, should you be...Ch. 7.C - Prob. 3ECh. 7.C - Prob. 4ECh. 7.C - Prob. 5ECh. 7.C - Prob. 6ECh. 7.C - The expected value to me of each raffle ticket I...Ch. 7.C - The expected value of each insurance policy our...Ch. 7.C - If you toss a coin four times, it’s much more...Ch. 7.C - I haven’t won in my last 25 pulls on the slot...Ch. 7.C - I haven’t won in my last 25 pulls on the slot...Ch. 7.C - I’ve lost S750 so far today on roulette. I’m going...Ch. 7.C - Understanding the Law of Large Numbers. Suppose...Ch. 7.C - Speedy Driver. Suppose a person who has a habit of...Ch. 7.C - Prob. 15ECh. 7.C - Expected Value Games. Find the expected value (to...Ch. 7.C - Prob. 17ECh. 7.C - Expected Value Games. Find the expected value (to...Ch. 7.C - Prob. 19ECh. 7.C - Prob. 20ECh. 7.C - Prob. 21ECh. 7.C - Expected Wait. A bus arrives at a bus stop at...Ch. 7.C - Gambler’s Fallacy and Coins. Suppose you play a...Ch. 7.C - Gambler’s Fallacy and Dice. Suppose you roll a die...Ch. 7.C - Can You Catch Up? Suppose you toss a fair coin 100...Ch. 7.C - Prob. 26ECh. 7.C - Prob. 27ECh. 7.C - Prob. 28ECh. 7.C - Prob. 29ECh. 7.C - Prob. 30ECh. 7.C - Prob. 31ECh. 7.C - Prob. 32ECh. 7.C - Prob. 33ECh. 7.C - Prob. 34ECh. 7.C - Extra Points in Football. Football teams have the...Ch. 7.C - Roulette. When you bet $5 on the number 7 in...Ch. 7.C - Household Size. It is estimated that 57% of...Ch. 7.C - Prob. 38ECh. 7.C - Prob. 39ECh. 7.C - Prob. 40ECh. 7.C - Prob. 41ECh. 7.C - The Morality of Gambling. Republican Senator...Ch. 7.D - Prob. 1QQCh. 7.D - Prob. 2QQCh. 7.D - Prob. 3QQCh. 7.D - Prob. 4QQCh. 7.D - Prob. 5QQCh. 7.D - Based on Figure 7.11, besides the elderly, the...Ch. 7.D - Prob. 7QQCh. 7.D - Prob. 8QQCh. 7.D - Based on Figure 7.12, which statement is not...Ch. 7.D - Prob. 10QQCh. 7.D - Prob. 1ECh. 7.D - Prob. 2ECh. 7.D - Prob. 3ECh. 7.D - Prob. 4ECh. 7.D - Prob. 5ECh. 7.D - Prob. 6ECh. 7.D - Your life expectancy is the major factor in...Ch. 7.D - A 60-year-old has a shorter life expectancy than...Ch. 7.D - Prob. 9ECh. 7.D - Prob. 10ECh. 7.D - Prob. 11ECh. 7.D - Prob. 12ECh. 7.D - Prob. 13ECh. 7.D - Prob. 14ECh. 7.D - Prob. 15ECh. 7.D - 15–20: Causes of Death. Use Table 7.4, and assume...Ch. 7.D - Prob. 17ECh. 7.D - Prob. 18ECh. 7.D - 15–20: Causes of Death. Use Table 7.4, and assume...Ch. 7.D - 15–20: Causes of Death. Use Table 7.4, and assume...Ch. 7.D - Prob. 21ECh. 7.D - Prob. 22ECh. 7.D - Prob. 23ECh. 7.D - Prob. 24ECh. 7.D - Prob. 25ECh. 7.D - Prob. 26ECh. 7.D - Prob. 27ECh. 7.D - Prob. 28ECh. 7.D - Prob. 29ECh. 7.D - Prob. 30ECh. 7.D - Prob. 31ECh. 7.D - Prob. 32ECh. 7.D - Prob. 33ECh. 7.D - Aging population. The table shows the U S....Ch. 7.D - Prob. 35ECh. 7.D - Prob. 36ECh. 7.D - Prob. 37ECh. 7.D - Prob. 38ECh. 7.D - Prob. 39ECh. 7.E - 1. You are asked to create a 4-character password,...Ch. 7.E - Prob. 2QQCh. 7.E - A teacher has 28 students. and 5 them will be...Ch. 7.E - Prob. 4QQCh. 7.E - A soccer coach who has 15 children on her team...Ch. 7.E - One term in the denominator of the combinations...Ch. 7.E - Overall, number of different 4-person terns (order...Ch. 7.E - One in a stadium filled with 100,000 people is...Ch. 7.E - One in a stadium filled With people is chosen at...Ch. 7.E - There are 365 possible birthdays in a year. In a...Ch. 7.E - Prob. 1ECh. 7.E - Prob. 2ECh. 7.E - Prob. 3ECh. 7.E - 4. Explain What we mean When we that outcome is...Ch. 7.E - I used the permutations formula to determine how...Ch. 7.E - I used the combinations formula to determine how...Ch. 7.E - The number Of different possible batting orders...Ch. 7.E - It must my lucky day, the five-card poker hand I...Ch. 7.E - The probability that two people in a randomly...Ch. 7.E - Someone wins the lottery every week. so I figure...Ch. 7.E - Review of Factorials. use the skills covered in...Ch. 7.E - Review of Factorials. use the skills covered in...Ch. 7.E - Review of Factorials. use the skills covered in...Ch. 7.E - Prob. 14ECh. 7.E - Prob. 15ECh. 7.E - Prob. 16ECh. 7.E - Prob. 17ECh. 7.E - Prob. 18ECh. 7.E - Review off Factorials. use the skills covered in...Ch. 7.E - 11—22: Review off Factorials. use the skills...Ch. 7.E - 11—22: Review off Factorials. use the skills...Ch. 7.E - 11—22: Review off Factorials. use the skills...Ch. 7.E - Prob. 23ECh. 7.E - Counting Methods. Answer the following questions...Ch. 7.E - Prob. 25ECh. 7.E - Prob. 26ECh. 7.E - Prob. 27ECh. 7.E - Prob. 28ECh. 7.E - Prob. 29ECh. 7.E - Prob. 30ECh. 7.E - Prob. 31ECh. 7.E - Prob. 32ECh. 7.E - Counting Methods. Answer the following questions...Ch. 7.E - Prob. 34ECh. 7.E - Prob. 35ECh. 7.E - Prob. 36ECh. 7.E - Prob. 37ECh. 7.E - Prob. 38ECh. 7.E - Prob. 39ECh. 7.E - Prob. 40ECh. 7.E - Birthday Coincidences. Suppose you are part of a...Ch. 7.E - Birthday Coincidences. Suppose you are part of a...Ch. 7.E - 43. Ice Cream Shop. Josh and Ice Cream Shop Of-...Ch. 7.E - 44. Telephone Numbers. A ten-digit phone number in...Ch. 7.E - 45. Pizza Hype. Luigi; Pizza parlor advertises 56...Ch. 7.E - ZIP Codes. The US. Postal Service five-digit and...Ch. 7.E - 47 —54: Counting and Probability. Find the...Ch. 7.E - Prob. 48ECh. 7.E - Prob. 49ECh. 7.E - Prob. 50ECh. 7.E - Prob. 51ECh. 7.E - Prob. 52ECh. 7.E - Prob. 53ECh. 7.E - Prob. 54ECh. 7.E - Hot Streaks. Suppose that 2000 people are all...Ch. 7.E - Joe Record. One of longest-standing records in...Ch. 7.E - Prob. 57ECh. 7.E - Prob. 58ECh. 7.E - Prob. 59ECh. 7.E - Prob. 60ECh. 7.E - Prob. 61ECh. 7.E - Prob. 62ECh. 7.E - Prob. 63ECh. 7.E - Prob. 64E
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