An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Textbook Question
Chapter 3.5, Problem 1Q
Recall the game of Keno described in Question 3.2.26. The following are all the payoffs on a
| Number of Correct Guesses | Payoff | |
|
|
–$1 | .935 |
| 5 | 2 | .0514 |
| 6 | 18 | .0115 |
| 7 | 180 | .0016 |
| 8 | 1,300 |
|
| 9 | 2,600 |
|
| 10 | 10,000 |
|
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A recent survey of 400 americans asked whether or not parents do too much for their young adult children. The results of the survey are shown in the data file. a) Construct the frequency and relative frequency distributions. How many respondents felt that parents do too much for their adult children? What proportion of respondents felt that parents do too little for their adult children? b) Construct a pie chart. Summarize the findings
The average number of minutes Americans commute to work is 27.7 minutes (Sterling's Best Places, April 13, 2012). The average commute time in minutes for 48 cities are as follows:
Click on the datafile logo to reference the data.
DATA file
Albuquerque
23.3
Jacksonville
26.2
Phoenix
28.3
Atlanta
28.3
Kansas City
23.4
Pittsburgh
25.0
Austin
24.6
Las Vegas
28.4
Portland
26.4
Baltimore
32.1
Little Rock
20.1
Providence
23.6
Boston
31.7
Los Angeles
32.2
Richmond
23.4
Charlotte
25.8
Louisville
21.4
Sacramento
25.8
Chicago
38.1
Memphis
23.8
Salt Lake City
20.2
Cincinnati
24.9
Miami
30.7
San Antonio
26.1
Cleveland
26.8
Milwaukee
24.8
San Diego
24.8
Columbus
23.4
Minneapolis
23.6
San Francisco
32.6
Dallas
28.5
Nashville
25.3
San Jose
28.5
Denver
28.1
New Orleans
31.7
Seattle
27.3
Detroit
29.3
New York
43.8
St. Louis
26.8
El Paso
24.4
Oklahoma City
22.0
Tucson
24.0
Fresno
23.0
Orlando
27.1
Tulsa
20.1
Indianapolis
24.8
Philadelphia
34.2
Washington, D.C.
32.8
a. What is the mean commute time for…
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds.
Click on the datafile logo to reference the data.
DATA file
Type of Fund
Domestic Equity
Number of Funds
Total Return (%)
9191
4.65
International Equity
2621
18.15
Hybrid
1419
2900
11.36
6.75
Specialty Stock
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)
%
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…
Chapter 3 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 3.2 - An investment analyst has tracked a certain...Ch. 3.2 - In a nuclear reactor, the fission process is...Ch. 3.2 - In 2009 a donor who insisted on anonymity gave...Ch. 3.2 - An entrepreneur owns six corporations, each with...Ch. 3.2 - The probability is 0.10 that ball bearings in a...Ch. 3.2 - Suppose that since the early 1950s some...Ch. 3.2 - Doomsday Airlines (Come Take the Flight of Your...Ch. 3.2 - Two lighting systems are being proposed for an...Ch. 3.2 - The great English diarist Samuel Pepys asked his...Ch. 3.2 - The gunner on a small assault boat fires six...
Ch. 3.2 - If a family has four children, is it more likely...Ch. 3.2 - Experience has shown that only 13 of all patients...Ch. 3.2 - Transportation to school for a rural countys...Ch. 3.2 - The captain of a Navy gunboat orders a volley of...Ch. 3.2 - A computer has generated seven random numbers over...Ch. 3.2 - Listed in the following table is the length...Ch. 3.2 - Redo Example 3.2.4 assuming n=12 and p=0.3.Ch. 3.2 - Prob. 18QCh. 3.2 - Prob. 19QCh. 3.2 - A corporate board contains twelve members. The...Ch. 3.2 - One of the popular tourist attractions in Alaska...Ch. 3.2 - A city has 4050 children under the age of ten,...Ch. 3.2 - Country A inadvertently launches ten guided...Ch. 3.2 - Anne is studying for a history exam covering the...Ch. 3.2 - Each year a college awards five merit-based...Ch. 3.2 - Keno is a casino game in which the player has a...Ch. 3.2 - A display case contains thirty-five gems, of which...Ch. 3.2 - Consider an urn with r red balls and w white...Ch. 3.2 - Prob. 29QCh. 3.2 - Prob. 30QCh. 3.2 - Prob. 31QCh. 3.2 - Prob. 32QCh. 3.2 - Prob. 33QCh. 3.2 - Some nomadic tribes, when faced with a...Ch. 3.2 - Suppose a population contains n1 objects of one...Ch. 3.2 - Prob. 36QCh. 3.3 - Prob. 1QCh. 3.3 - Repeat Question 3.3.1 for the case where the two...Ch. 3.3 - Suppose a fair die is tossed three times. Let X be...Ch. 3.3 - Suppose a fair die is tossed three times. Let X be...Ch. 3.3 - A fair coin is tossed three times. Let X be the...Ch. 3.3 - Suppose die one has spots 1, 2, 2, 3, 3, 4 and die...Ch. 3.3 - Suppose a particle moves along the x-axis...Ch. 3.3 - How would the pdf asked for in Question 3.3.7 be...Ch. 3.3 - Suppose that five people, including you and a...Ch. 3.3 - Prob. 10QCh. 3.3 - Prob. 11QCh. 3.3 - Prob. 12QCh. 3.3 - A fair die is rolled four times. Let the random...Ch. 3.3 - At the points x=0,1,...,6, the cdf for the...Ch. 3.3 - Find the pdf for the infinite-valued discrete...Ch. 3.3 - Recall the game of Fantasy Five from Example...Ch. 3.4 - Suppose fY(y)=4y3,0y1. Find P(0Y12).Ch. 3.4 - For the random variable Y with pdf...Ch. 3.4 - Let fY(y)=23y2,1y1. Find P(|Y12|14). Draw a graph...Ch. 3.4 - For persons infected with a certain form of...Ch. 3.4 - For a high-risk driver, the time in days between...Ch. 3.4 - Let n be a positive integer. Show that...Ch. 3.4 - Find the cdf for the random variable Y given in...Ch. 3.4 - If Y is an exponential random variable,...Ch. 3.4 - If the pdf for Y is fY(y)={0,|y|11|y|,|y|1 find...Ch. 3.4 - Prob. 10QCh. 3.4 - Prob. 11QCh. 3.4 - Prob. 12QCh. 3.4 - Prob. 13QCh. 3.4 - Prob. 14QCh. 3.4 - The logistic curve F(y)=11+ey,y, can represent a...Ch. 3.4 - Prob. 16QCh. 3.4 - Prob. 17QCh. 3.4 - Let Y be a random variable denoting the age at...Ch. 3.5 - Recall the game of Keno described in Question...Ch. 3.5 - The roulette wheels in Monte Carlo typically have...Ch. 3.5 - The pdf describing the daily profit, X, earned by...Ch. 3.5 - In the game of redball, two drawings are made...Ch. 3.5 - Suppose a life insurance company sells a $50,000,...Ch. 3.5 - A manufacturer has one hundred memory chips in...Ch. 3.5 - Records show that 642 new students have just...Ch. 3.5 - Prob. 8QCh. 3.5 - Recall Question 3.4.4, where the length of time Y...Ch. 3.5 - Let the random variable Y have the uniform...Ch. 3.5 - Show that the expected value associated with the...Ch. 3.5 - Show that fY(y)=1y2,y1 is a valid pdf but that Y...Ch. 3.5 - Based on recent experience, ten-year-old passenger...Ch. 3.5 - Prob. 14QCh. 3.5 - A city has 74,806 registered automobiles. Each is...Ch. 3.5 - Regulators have found that twenty-three of the...Ch. 3.5 - An urn contains four chips numbered 1 through 4....Ch. 3.5 - A fair coin is tossed three times. Let the random...Ch. 3.5 - Prob. 19QCh. 3.5 - For the St. Petersburg problem (Example 3.5.5),...Ch. 3.5 - Prob. 21QCh. 3.5 - Prob. 22QCh. 3.5 - Suppose that two evenly matched teams are playing...Ch. 3.5 - An urn contains one white chip and one black chip....Ch. 3.5 - Prob. 25QCh. 3.5 - Prob. 26QCh. 3.5 - Find the median for each of the following pdfs:...Ch. 3.5 - Suppose X is a binomial random variable with n=10...Ch. 3.5 - A typical days production of a certain electronic...Ch. 3.5 - Let Y have probability density function...Ch. 3.5 - Prob. 31QCh. 3.5 - A box is to be constructed so that its height is...Ch. 3.5 - Prob. 33QCh. 3.5 - If Y has probability density function fY(y)=2y,0y1...Ch. 3.5 - Prob. 35QCh. 3.5 - Prob. 36QCh. 3.6 - Find Var(X) for the urn problem of Example 3.6.1...Ch. 3.6 - Find the variance of Y if...Ch. 3.6 - Ten equally qualified applicants, six men and four...Ch. 3.6 - A certain hospitalization policy pays a cash...Ch. 3.6 - Use Theorem 3.6.1 to find the variance of the...Ch. 3.6 - If fY(y)=2yk2,0yk for what value of k does...Ch. 3.6 - Calculate the standard deviation, , for the random...Ch. 3.6 - Consider the pdf defined by fY(y)=2y3,y1 Show that...Ch. 3.6 - Frankie and Johnny play the following game....Ch. 3.6 - Let Y be a random variable whose pdf is given by...Ch. 3.6 - Suppose that Y is an exponential random variable,...Ch. 3.6 - Suppose that Y is an exponential random variable...Ch. 3.6 - Let X be a random variable with finite mean ....Ch. 3.6 - Suppose the charge for repairing an automobile...Ch. 3.6 - If Y denotes a temperature recorded in degrees...Ch. 3.6 - Prob. 16QCh. 3.6 - Suppose U is a uniform random variable over [0,1]....Ch. 3.6 - Recovering small quantities of calcium in the...Ch. 3.6 - Let Y be a uniform random variable defined over...Ch. 3.6 - Find the coefficient of skewness for an...Ch. 3.6 - Calculate the coefficient of kurtosis for a...Ch. 3.6 - Suppose that W is a random variable for which...Ch. 3.6 - If Y=aX+b,a0, show that Y has the same...Ch. 3.6 - Let Y be the random variable of Question 3.4.6,...Ch. 3.6 - Prob. 25QCh. 3.7 - Prob. 1QCh. 3.7 - Prob. 2QCh. 3.7 - Prob. 3QCh. 3.7 - Find c if fX,Y(x,y)=cxy for X and Y defined over...Ch. 3.7 - Prob. 5QCh. 3.7 - Four cards are drawn from a standard poker deck....Ch. 3.7 - An advisor looks over the schedules of his fifty...Ch. 3.7 - Consider the experiment of tossing a fair coin...Ch. 3.7 - Suppose that two fair dice are tossed one time....Ch. 3.7 - Let X be the time in days between a car accident...Ch. 3.7 - Let X and Y have the joint pdf...Ch. 3.7 - A point is chosen at random from the interior of a...Ch. 3.7 - Find P(X2Y) if fX,Y(x,y)=x+y for X and Y each...Ch. 3.7 - Prob. 14QCh. 3.7 - A point is chosen at random from the interior of a...Ch. 3.7 - Prob. 16QCh. 3.7 - Find the marginal pdfs of X and Y for the joint...Ch. 3.7 - Prob. 18QCh. 3.7 - For each of the following joint pdfs, find fX(x)...Ch. 3.7 - For each of the following joint pdfs, find fX(x)...Ch. 3.7 - Prob. 21QCh. 3.7 - Prob. 22QCh. 3.7 - Prob. 23QCh. 3.7 - Prob. 24QCh. 3.7 - Consider the experiment of simultaneously tossing...Ch. 3.7 - Prob. 26QCh. 3.7 - For each of the following joint pdfs, find...Ch. 3.7 - Prob. 28QCh. 3.7 - Prob. 29QCh. 3.7 - Prob. 30QCh. 3.7 - Given that FX,Y(x,y)=k(4x2y2+5xy4),0x1,0y1, find...Ch. 3.7 - Prob. 32QCh. 3.7 - Prob. 33QCh. 3.7 - Prob. 34QCh. 3.7 - Prob. 35QCh. 3.7 - Prob. 36QCh. 3.7 - Prob. 37QCh. 3.7 - Prob. 38QCh. 3.7 - Prob. 39QCh. 3.7 - Suppose that each of two urns has four chips,...Ch. 3.7 - Let X and Y be random variables with joint pdf...Ch. 3.7 - Are the random variables X and Y independent if...Ch. 3.7 - Prob. 43QCh. 3.7 - Find the joint cdf of the independent random...Ch. 3.7 - Prob. 45QCh. 3.7 - Prob. 46QCh. 3.7 - Prob. 47QCh. 3.7 - Prob. 48QCh. 3.7 - Prob. 49QCh. 3.7 - Prob. 50QCh. 3.7 - Suppose that X1,X2,X3, and X4 are independent...Ch. 3.7 - Prob. 52QCh. 3.8 - Prob. 1QCh. 3.8 - Prob. 2QCh. 3.8 - Prob. 3QCh. 3.8 - Prob. 4QCh. 3.8 - Prob. 5QCh. 3.8 - Prob. 6QCh. 3.8 - Prob. 7QCh. 3.8 - Prob. 8QCh. 3.8 - Prob. 9QCh. 3.8 - Prob. 10QCh. 3.8 - Prob. 11QCh. 3.8 - Prob. 12QCh. 3.8 - Prob. 13QCh. 3.9 - Prob. 1QCh. 3.9 - Prob. 2QCh. 3.9 - Suppose that fX,Y(x,y)=23(x+2y),0x1,0y1 [recall...Ch. 3.9 - Marksmanship competition at a certain level...Ch. 3.9 - Suppose that Xi is a random variable for which...Ch. 3.9 - Prob. 6QCh. 3.9 - Prob. 7QCh. 3.9 - Suppose two fair dice are tossed. Find the...Ch. 3.9 - Prob. 9QCh. 3.9 - Suppose that X and Y are both uniformly...Ch. 3.9 - Prob. 11QCh. 3.9 - Prob. 12QCh. 3.9 - Prob. 13QCh. 3.9 - Prob. 14QCh. 3.9 - Prob. 15QCh. 3.9 - Let X and Y be random variables with...Ch. 3.9 - Suppose that fX,Y(x,y)=2e(x+y),0x,0y. Find...Ch. 3.9 - Prob. 18QCh. 3.9 - Prob. 19QCh. 3.9 - Let X be a binomial random variable based on n...Ch. 3.9 - Prob. 21QCh. 3.9 - Prob. 22QCh. 3.9 - Prob. 23QCh. 3.9 - A gambler plays n hands of poker. If he wins the...Ch. 3.10 - Suppose the length of time, in minutes, that you...Ch. 3.10 - A random sample of size n=6 is taken from the pdf...Ch. 3.10 - What is the probability that the larger of two...Ch. 3.10 - Prob. 4QCh. 3.10 - Prob. 5QCh. 3.10 - Let Y1,Y2,...,Yn be a random sample from the...Ch. 3.10 - Calculate P(0.6Y40.7) if a random sample of size 6...Ch. 3.10 - A random sample of size n=5 is drawn from the pdf...Ch. 3.10 - Prob. 9QCh. 3.10 - Suppose that n observations are chosen at random...Ch. 3.10 - In a certain large metropolitan area, the...Ch. 3.10 - Consider a system containing n components, where...Ch. 3.10 - Prob. 13QCh. 3.10 - Prob. 14QCh. 3.10 - Prob. 15QCh. 3.10 - Suppose a device has three independent components,...Ch. 3.11 - Prob. 1QCh. 3.11 - Suppose a die is rolled six times. Let X be the...Ch. 3.11 - Prob. 3QCh. 3.11 - Five cards are dealt from a standard poker deck....Ch. 3.11 - Given that two discrete random variables X and Y...Ch. 3.11 - Prob. 6QCh. 3.11 - Suppose X, Y, and Z have a trivariate distribution...Ch. 3.11 - Prob. 8QCh. 3.11 - Let X and Y be independent Poisson random...Ch. 3.11 - Prob. 10QCh. 3.11 - Prob. 11QCh. 3.11 - Prob. 12QCh. 3.11 - Prob. 13QCh. 3.11 - Prob. 14QCh. 3.11 - Prob. 15QCh. 3.11 - Prob. 16QCh. 3.11 - Prob. 17QCh. 3.11 - Prob. 18QCh. 3.11 - Prob. 19QCh. 3.11 - Prob. 20QCh. 3.11 - For continuous random variables X and Y, prove...Ch. 3.12 - Let X be a random variable with pdf pX(k)=1/n, for...Ch. 3.12 - Two chips are drawn at random and without...Ch. 3.12 - Prob. 3QCh. 3.12 - Find the moment-generating function for the...Ch. 3.12 - Which pdfs would have the following...Ch. 3.12 - Prob. 6QCh. 3.12 - The random variable X has a Poisson distribution...Ch. 3.12 - Prob. 8QCh. 3.12 - Prob. 9QCh. 3.12 - Find E(Y4) if Y is an exponential random variable...Ch. 3.12 - Prob. 11QCh. 3.12 - Prob. 12QCh. 3.12 - Prob. 13QCh. 3.12 - Prob. 14QCh. 3.12 - Prob. 15QCh. 3.12 - Find the variance of Y if MY(t)=e2t/(1t2).Ch. 3.12 - Prob. 17QCh. 3.12 - Let Y1,Y2, and Y3 be independent random variables,...Ch. 3.12 - Use Theorems 3.12.2 and 3.12.3 to determine which...Ch. 3.12 - Calculate P(X2) if MX(t)=(14+34et)5.Ch. 3.12 - Suppose that Y1,Y2,...,Yn is a random sample of...Ch. 3.12 - Suppose the moment-generating function for a...Ch. 3.12 - Suppose that X is a Poisson random variable, where...Ch. 3.12 - Prob. 24Q
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