Mathematical Statistics with Applications
7th Edition
ISBN: 9781133384380
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
Publisher: Cengage Learning US
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Textbook Question
Chapter 9.6, Problem 76E
Let X1, X2, X3,… be independent Bernoulli random variables such that P (Xi = 1) = p and P (Xi = 0) = 1 − p for each i = 1, 2, 3,…. Let the random variable Y denote the number of trials necessary to obtain the first success—that is, the value of i for which Xi = 1 first occurs. Then Y has a geometric distribution with P (Y = y) = (1 − p)y−1 p, for y = 1, 2, 3,…. Find the method-of-moments estimator of p based on this single observation Y.
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Techniques QUAT6221 2025 PT B...
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Activities Assessments Class Progress lIE Library • Help v
The table below shows the prices (R) and quantities (kg) of rice, meat and potatoes items bought during 2013 and 2014:
2013
2014
P1Qo
PoQo
Q1Po P1Q1
Price
Ро
Quantity
Qo
Price
P1
Quantity
Q1
Rice
7
80
6
70
480
560
490
420
Meat
30
50
35
60
1 750
1 500
1 800
2 100
Potatoes
3
100
3
100
300
300
300
300
TOTAL
40
230
44
230
2 530
2 360
2 590
2 820
Instructions:
1 Corall dawn to tha bottom of thir ceraan urina se se tha haca nariad in archerca antarand cubmit
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ENG US
口X
2025/05
The table below indicates the number of years of experience of a sample of employees who work on a particular production line and the corresponding number of units of a good that each employee produced last month.
Years of Experience (x)
Number of Goods (y)
11
63
5
57
1
48
4
54
45
3
51
Q.1.1 By completing the table below and then applying the relevant formulae, determine the line of best fit for this bivariate data set.
Do NOT change the units for the variables.
X
y
X2
xy
Ex=
Ey=
EX2
EXY=
Q.1.2 Estimate the number of units of the good that would have been produced last month by an employee with 8 years of experience.
Q.1.3 Using your calculator, determine the coefficient of correlation for the data set.
Interpret your answer.
Q.1.4 Compute the coefficient of determination for the data set.
Interpret your answer.
Q.3.2 A sample of consumers was asked to name their favourite fruit. The results regarding the popularity of the different fruits are given in the following table.
Type of Fruit
Number of Consumers
Banana
25
Apple
20
Orange
5
TOTAL
50
Draw a bar chart to graphically illustrate the results given in the table.
Chapter 9 Solutions
Mathematical Statistics with Applications
Ch. 9.2 - Prob. 1ECh. 9.2 - Let Y1, Y2,, Yn denote a random sample from a...Ch. 9.2 - Let Y1, Y2, , Yn denote a random sample from the...Ch. 9.2 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 9.2 - Suppose that Y1, Y2, , Yn is a random sample from...Ch. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.3 - Applet Exercise How was Figure 9.1 obtained?...Ch. 9.3 - Applet Exercise Refer to Exercise 9.9. Scroll down...
Ch. 9.3 - Applet Exercise Refer to Exercises 9.9 and 9.10....Ch. 9.3 - Applet Exercise Refer to Exercise 9.11. What...Ch. 9.3 - Applet Exercise Refer to Exercises 9.99.12. Access...Ch. 9.3 - Applet Exercise Refer to Exercise 9.13. Scroll...Ch. 9.3 - Refer to Exercise 9.3. Show that both 1 and 2 are...Ch. 9.3 - Refer to Exercise 9.5. Is 22 a consistent...Ch. 9.3 - Suppose that X1, X2,, Xn and Y1, Y2,,Yn are...Ch. 9.3 - In Exercise 9.17, suppose that the populations are...Ch. 9.3 - Let Y1, Y2,,Yn denote a random sample from the...Ch. 9.3 - If Y has a binomial distribution with n trials and...Ch. 9.3 - Let Y1, Y2,, Yn be a random sample of size n from...Ch. 9.3 - Refer to Exercise 9.21. Suppose that Y1, Y2,, Yn...Ch. 9.3 - Refer to Exercise 9.21. Suppose that Y1, Y2,, Yn...Ch. 9.3 - Let Y1, Y2, Y3, Yn be independent standard normal...Ch. 9.3 - Suppose that Y1, Y2, , Yn denote a random sample...Ch. 9.3 - Prob. 26ECh. 9.3 - Use the method described in Exercise 9.26 to show...Ch. 9.3 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 9.3 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 9.3 - Let Y1, Y2, , Yn be independent random variables,...Ch. 9.3 - Prob. 31ECh. 9.3 - Let Y1, Y2, , Yn denote a random sample from the...Ch. 9.3 - An experimenter wishes to compare the numbers of...Ch. 9.3 - Prob. 34ECh. 9.3 - Let Y1, Y2, be a sequence of random variables with...Ch. 9.3 - Suppose that Y has a binomial distribution based...Ch. 9.4 - Prob. 37ECh. 9.4 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - Prob. 40ECh. 9.4 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - If Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - Prob. 43ECh. 9.4 - Let Y1, Y2, , Yn denote independent and...Ch. 9.4 - Suppose that Y1, Y2, , Yn is a random sample from...Ch. 9.4 - If Y1, Y2,, Yn denote a random sample from an...Ch. 9.4 - Refer to Exercise 9.43. If is known, show that...Ch. 9.4 - Refer to Exercise 9.44. If is known, show that...Ch. 9.4 - Let Y1, Y2, . . . , Yn denote a random sample from...Ch. 9.4 - Let Y1, Y2, . . . , Yn denote a random sample from...Ch. 9.4 - Prob. 51ECh. 9.4 - Prob. 52ECh. 9.4 - Prob. 53ECh. 9.4 - Prob. 54ECh. 9.4 - Let Y1, Y2, . . . , Yn denote independent and...Ch. 9.5 - Refer to Exercise 9.38(b). Find an MVUE of 2. 9.38...Ch. 9.5 - Refer to Exercise 9.18. Is the estimator of 2...Ch. 9.5 - Refer to Exercise 9.40. Use i=1nYi2 to find an...Ch. 9.5 - The number of breakdowns Y per day for a certain...Ch. 9.5 - Prob. 60ECh. 9.5 - Refer to Exercise 9.49. Use Y(n) to find an MVUE...Ch. 9.5 - Refer to Exercise 9.51. Find a function of Y(1)...Ch. 9.5 - Prob. 63ECh. 9.5 - Let Y1, Y2, , Yn be a random sample from a normal...Ch. 9.5 - In this exercise, we illustrate the direct use of...Ch. 9.5 - The likelihood function L(y1,y2,,yn|) takes on...Ch. 9.5 - Refer to Exercise 9.66. Suppose that a sample of...Ch. 9.5 - Prob. 68ECh. 9.6 - Prob. 69ECh. 9.6 - Suppose that Y1, Y2, , Yn constitute a random...Ch. 9.6 - If Y1, Y2, , Yn denote a random sample from the...Ch. 9.6 - If Y1, Y2, , Yn denote a random sample from the...Ch. 9.6 - An urn contains black balls and N white balls....Ch. 9.6 - Let Y1, Y2,, Yn constitute a random sample from...Ch. 9.6 - Prob. 75ECh. 9.6 - Let X1, X2, X3, be independent Bernoulli random...Ch. 9.6 - Let Y1, Y2,, Yn denote independent and identically...Ch. 9.6 - Let Y1, Y2,, Yn denote independent and identically...Ch. 9.6 - Let Y1, Y2,, Yn denote independent and identically...Ch. 9.7 - Suppose that Y1, Y2,, Yn denote a random sample...Ch. 9.7 - Suppose that Y1, Y2, , Yn denote a random sample...Ch. 9.7 - Prob. 82ECh. 9.7 - Suppose that Y1, Y2, , Yn constitute a random...Ch. 9.7 - Prob. 84ECh. 9.7 - Let Y1, Y2,, Yn denote a random sample from the...Ch. 9.7 - Suppose that X1, X2, , Xm, representing yields per...Ch. 9.7 - A random sample of 100 voters selected from a...Ch. 9.7 - Prob. 88ECh. 9.7 - It is known that the probability p of tossing...Ch. 9.7 - A random sample of 100 men produced a total of 25...Ch. 9.7 - Find the MLE of based on a random sample of size...Ch. 9.7 - Prob. 92ECh. 9.7 - Prob. 93ECh. 9.7 - Suppose that is the MLE for a parameter . Let t()...Ch. 9.7 - A random sample of n items is selected from the...Ch. 9.7 - Consider a random sample of size n from a normal...Ch. 9.7 - The geometric probability mass function is given...Ch. 9.8 - Refer to Exercise 9.97. What is the approximate...Ch. 9.8 - Consider the distribution discussed in Example...Ch. 9.8 - Suppose that Y1, Y2, . . . , Yn constitute a...Ch. 9.8 - Let Y1, Y2, . . . , Yn denote a random sample of...Ch. 9.8 - Refer to Exercises 9.97 and 9.98. If a sample of...Ch. 9 - Prob. 103SECh. 9 - Prob. 104SECh. 9 - Refer to Exercise 9.38(b). Under the conditions...Ch. 9 - Prob. 106SECh. 9 - Suppose that a random sample of length-of-life...Ch. 9 - The MLE obtained in Exercise 9.107 is a function...Ch. 9 - Prob. 109SECh. 9 - Refer to Exercise 9.109. a Find the MLE N2 of N. b...Ch. 9 - Refer to Exercise 9.110. Suppose that enemy tanks...Ch. 9 - Let Y1, Y2, . . . , Yn denote a random sample from...
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