Probability And Statistical Inference (10th Edition)
10th Edition
ISBN: 9780135189399
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 5.3, Problem 15E
In considering medical insurance for a certain operation, let X equal the amount (in dollars) paid for the doctor and let Y equal the amount paid to the hosp ital. In the past, the variances have been
Due to increased expenses, it was decided to increase the doctor’s fee by $500 and increase the hospital charge Y by 8%. Calculate the variance of
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Chapter 5 Solutions
Probability And Statistical Inference (10th Edition)
Ch. 5.1 - Let X have a geometric distribution with parameter...Ch. 5.1 - Suppose that X is a continuous random variable...Ch. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Let X have a gamma distribution with =3 and =2....Ch. 5.1 - The pdf of X is f(x)=2x,0x1. (a) Find the cdf of...Ch. 5.1 - Prob. 7ECh. 5.1 - Let X have a logistic distribution with pdf...Ch. 5.1 - A sum of $50000 is invested at a rate R, selected...Ch. 5.1 - The lifetime (in years) of a manufactured product...
Ch. 5.1 - Statisticians frequently use the extreme extreme...Ch. 5.1 - Prob. 12ECh. 5.1 - Let X have a Cauchy distribution. Find (a) P(X1)....Ch. 5.1 - Let f(x)=1[(1+x2)],x, be the pdf of the Cauchy...Ch. 5.1 - If X is N(,2), then M(t)=E(etX)=exp(t+2t22),t. We...Ch. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - (a) Let X be a continuous random variable with...Ch. 5.2 - Let X1,X2, denote two independent random...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Prob. 3ECh. 5.2 - Let the distribution of W be F(9, 24). Find the...Ch. 5.2 - Let the distribution of W be F(8. 4). Find the...Ch. 5.2 - Let X1 and X2 have independent gamma distributions...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Let X have a beta distribution with parameters ...Ch. 5.2 - Determine the constant c such that...Ch. 5.2 - When and are integers and0p1, we have...Ch. 5.2 - Evaluate 00.4(7)(4)(3)y3(1y)2dy (a) Using...Ch. 5.2 - Let W1,W2 be independent, each with a Cauchy...Ch. 5.2 - Let X1, X2 be independent random variables...Ch. 5.2 - Prob. 14ECh. 5.2 - In Example 5.2-6, verify that the given...Ch. 5.2 - Show that if W has an F(r1,r2) distribution, then...Ch. 5.2 - Let W have an F distribution with parameters r1...Ch. 5.3 - Let X1 and X2 be independent Poisson random...Ch. 5.3 - Let X1 and X2 be independent random variables with...Ch. 5.3 - Let X1 and X2 be independent random variables with...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - Let X1 and X2 be observations of a random sample...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - The distributions of incomes in two Cities follow...Ch. 5.3 - Prob. 8ECh. 5.3 - Let X1,X2,...Xn be a random sample (of size n)...Ch. 5.3 - Let X1,X2,X3 denote a random sample of size n= 3...Ch. 5.3 - Let X1,X2,X3 be three independent random variables...Ch. 5.3 - Let X1,X2,X3 be a random sample of size n=3 from...Ch. 5.3 - Prob. 13ECh. 5.3 - Let X1,X2,X3 be independent random variables that...Ch. 5.3 - In considering medical insurance for a certain...Ch. 5.3 - The lifetime in months of a certain part has a...Ch. 5.3 - Two components operate in parallel in a device, so...Ch. 5.3 - Prob. 18ECh. 5.3 - Flip n=8 fair coins and remove all that came up...Ch. 5.3 - Prob. 20ECh. 5.4 - Let X1+X2+X3 be a random sample of size 3 from the...Ch. 5.4 - Let X1 and X2 have independent distributions...Ch. 5.4 - Prob. 3ECh. 5.4 - Generalize Exercise 5.4-3 by showing that the sum...Ch. 5.4 - Let Z1,Z2,....,Z7 be a random sample from the...Ch. 5.4 - Let X1,X2,X3,X4,X5 be a random sample of size 5...Ch. 5.4 - Let X1,X2,X3 denote a random sample of size 3 from...Ch. 5.4 - Let W=X1+X2+...+Xh, a sum of h mutually...Ch. 5.4 - Let X and Y, with respective pmfs f(x) and g(y),...Ch. 5.4 - Let X equal the outcome when a fair four-sided die...Ch. 5.4 - Let X and Y equal the outcomes when two fair...Ch. 5.4 - Let X and Y be the outcomes when a pair of fair...Ch. 5.4 - Let X1,X2,...,X8 be a random sample from a...Ch. 5.4 - The number of accidents in a period of one week...Ch. 5.4 - Given a fair four-sided die, let Y equal the...Ch. 5.4 - The number X of sick days taken during a year by...Ch. 5.4 - In a study concerning a new treatment of a certain...Ch. 5.4 - The number of cracks on a highway averages 0.5 per...Ch. 5.4 - A doorman at a hotel is trying to get three taxic...Ch. 5.4 - The time X in minutes of a visit to a...Ch. 5.4 - Let X and Y be independent with distributions...Ch. 5.4 - Let X1 and X2 be two independent random variables....Ch. 5.4 - Let X be N(0,1). Use the mgf technique to show...Ch. 5.4 - Let X1,X2,X3,X4 be a random sample from a x2(r)...Ch. 5.5 - Let X1,X2...,X16, be a random sample from a normal...Ch. 5.5 - Let X be N(50,36). Using the same set of axes,...Ch. 5.5 - Let X equal the widest diameter (in millimeters)...Ch. 5.5 - Let X equal the weight of the soap in a 6-pound...Ch. 5.5 - Let X equal the weight (in grams) of a nail of the...Ch. 5.5 - Let X1,X2,...,X100 be a random sample from N(,4),...Ch. 5.5 - Suppose that the distribution of the weight of a...Ch. 5.5 - Let X denote the wing length in millimeters of a...Ch. 5.5 - Suppose that the length of life in hours (say, X)...Ch. 5.5 - A consumer buys n light bulbs, each of which has a...Ch. 5.5 - A marketing research firm suggests to a comp any...Ch. 5.5 - Let the independent random variables X1 and X2 be...Ch. 5.5 - Prob. 13ECh. 5.5 - Let T have at distribution with r degrees of freed...Ch. 5.5 - Let the distribution of T be t(17). Find (a)...Ch. 5.5 - Prob. 16ECh. 5.6 - Let X be the mean of a random sample of size 12...Ch. 5.6 - Let Y=X1+X2+....+X15 be the sum of a random sample...Ch. 5.6 - Let X be the mean of a random sample of size 36...Ch. 5.6 - Approximate P(39.75X41.25), where X is the mean of...Ch. 5.6 - Let X1,X2,...,X18 be a random sample of size 18...Ch. 5.6 - A random sample of size ii = 18 is taken from the...Ch. 5.6 - Let X equal the maximal oxygen intake of a human...Ch. 5.6 - Let X equal the weight in grams of a miniature...Ch. 5.6 - In Example 5.6-4, with n=4, compute P(1.73.2) and...Ch. 5.6 - Prob. 10ECh. 5.6 - The tensile strength X of paper, in pounds per...Ch. 5.6 - At certain times during the year, a bus company...Ch. 5.6 - Prob. 13ECh. 5.6 - Suppose that the sick leave taken by the typical...Ch. 5.7 - Let the distribution of Y be b(25,1/2). Find the...Ch. 5.7 - Suppose that among gifted seventh-graders who...Ch. 5.7 - A public opinion poll in Southern California was...Ch. 5.7 - Let X equal the number out of n=48 mature aster...Ch. 5.7 - Let X1,X2,...,X48 be a random sample of size 48...Ch. 5.7 - In adults, the pneumococcus bacterium causes 70%...Ch. 5.7 - Let X equal the number of alpha particles emitted...Ch. 5.7 - A candy maker produces mints that have a label...Ch. 5.7 - Let X1,X2,...,X30 be a random sample of size 30...Ch. 5.7 - Prob. 10ECh. 5.7 - On January 1 of a given year, a college basketball...Ch. 5.7 - If X is b(100,0.1), find the approximate value of...Ch. 5.7 - Let X1,X2,...,X36 be a random sample of size 36...Ch. 5.7 - A die is rolled 24 independent times. Let V be the...Ch. 5.7 - In the United States, the probability that a child...Ch. 5.7 - Let X equal the sum of n=100 Bernoulli trials....Ch. 5.7 - The number of trees in one acre has a Poisson...Ch. 5.7 - Assume that the background noise X of a digital...Ch. 5.7 - A company has a one-year group life policy that...Ch. 5.8 - If X is a random variable with mean 33 and...Ch. 5.8 - If E(X)=17 and E(X2)=298, use Chebyshevs...Ch. 5.8 - Let X denote the outcome when a fair die is...Ch. 5.8 - If Y is b(n,0.5), give a lower bound for...Ch. 5.8 - If the distribution of Y is b(n,0.25), give a...Ch. 5.8 - Let X be the mean of a random sample of size n=15...Ch. 5.8 - Suppose that W is a continuous random variable...Ch. 5.9 - Let Y be the number of defectives in a box of 50...Ch. 5.9 - The probability that a certain type of inoculation...Ch. 5.9 - Let S2 be the sample variance of a random sample...Ch. 5.9 - Let Y be x2(n). Use the central limit theorem to...Ch. 5.9 - Let Y have a Poisson distribution with mean 3n....
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- Find the mean hourly cost when the cell phone described above is used for 240 minutes.arrow_forwardFor 50 students of a class the regression equation of marks in Statistics (X) on the marks in Accountancy (Y) is 3Y – 5 X + 180 = 0. The mean marks of Accountancy is 44 and variance of marks in Statistics is 9/16th of the variance of marks in Accountancy. Find the mean marks of Statistics and the coefficient of correlation between marks in two subjects.arrow_forward1 The menu at a café is shown below. Main coursе Dessert Fish and Chips $3 Ice Cream $1 Apple Pie Sponge Pudding Spaghetti $3.50 $1.50 Pizza $4 $2 Steak and Chips $5.50 The owner of the café says that all the main-course dishes sell equally well, as do all the desserts, and that customers' choice of dessert is not influenced by the main course they have just eaten.arrow_forward
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- The following table was generated from the sample data of 1010 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1x1) is the number of hours unsupervised each night, and the second independent variable (x2x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 57.968435 7.227955 8.020032 0.000201 Hours Unsupervised 5.131630 1.314283 3.904510 0.007943 Hours Playing Video Games 1.067855 1.615039 0.661194 0.533040 Indicate if any of the independent variables could be eliminated at thearrow_forwardThe following table was generated from the sample data of 1010 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1x1) is the number of hours unsupervised each night, and the second independent variable (x2x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 57.968435 7.227955 8.020032 0.000201 Hours Unsupervised 5.131630 1.314283 3.904510 0.007943 Hours Playing Video Games 1.067855 1.615039 0.661194 0.533040 Write the multiple regression equation for the computer output given. Round your answers to three decimal places.arrow_forwardThe following table was generated from the sample data of 1010 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1x1) is the number of hours unsupervised each night, and the second independent variable (x2x2) is the number of hours of video games each night. Intercept 64.821745 4.918050 13.180375 0.000012 Hours Unsupervised -1.691108 1.396989 -1.210538 0.271590 Hours Playing Video Games 6.796882 1.515248 4.485657 0.004167 Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places. Step 2 of 2: Indicate if any of the independent variables could be eliminated at the 0.050.05 level of significance.arrow_forward
- A firm purchases two types of industrial chemicals. Type I chemical costs $3 per gallon, whereas type II costs $5 per gallon. The mean and variance for the number of gallons of type I chemical purchased, Y,, are 40 and 4, respectively. The amount of type II chemical purchased, Y2, has E(Y2) = 65 gallons and V(Y2) = 8. Assume that Y, and Y2 are independent and find the mean and variance of the total amount of money spent per week on the two chemicals.arrow_forwardIf the average of z and 5z is 30, what is the value of a?arrow_forwardThe following table was generated from the sample data of 10 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1) is the number of hours unsupervised each night, and the second independent variable (x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 62.711817 4.607133 13.611896 0.000010 Hours Unsupervised 0.635048 0.915495 0.693666 0.513836 Hours Playing Video Games 7.528738 1.296727 5.805955 0.001145 Copy Data Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places. Answer 田 Tables 国 Keypad How to enter your answer (opens in new window) Keyboard Shortcuts X +arrow_forward
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