Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 9, Problem 109SE
a.
To determine
Obtain the method of moments estimator
b.
To determine
Obtain
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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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- Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADOarrow_forwardSuppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?arrow_forwardA normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forward
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