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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Chapter 5.8, Problem 4Q
To determine
To calculate: The squared-error loss Bayes estimate for the parameter
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Chapter 5 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 5.2 - A random sample of size...Ch. 5.2 - The number of red chips and white chips in an urn...Ch. 5.2 - Use the sample y1=8.2,y2=9.1,y3=10.6, and y4=4.9...Ch. 5.2 - Suppose a random sample of size n is drawn from...Ch. 5.2 - Given that y1=2.3,y2=1.9, and y3=4.6 is a random...Ch. 5.2 - Use the method of maximum likelihood to estimate ...Ch. 5.2 - An engineer is creating a project scheduling...Ch. 5.2 - The following data show the number of occupants in...Ch. 5.2 - For the Major League Baseball seasons from 1950...Ch. 5.2 - (a) Based on the random sample...
Ch. 5.2 - Find the maximum likelihood estimate for in the...Ch. 5.2 - A random sample of size n is taken from the pdf...Ch. 5.2 - If the random variable Y denotes an individuals...Ch. 5.2 - For the negative binomial pdf...Ch. 5.2 - The exponential pdf is a measure of lifetimes of...Ch. 5.2 - Suppose a random sample of size n is drawn from a...Ch. 5.2 - Let y1,y2,...,yn be a random sample of size n from...Ch. 5.2 - Prob. 18QCh. 5.2 - A criminologist is searching through FBI files to...Ch. 5.2 - Prob. 20QCh. 5.2 - Suppose that Y1=8.3,Y2=4.9,Y3=2.6, and Y4=6.5 is a...Ch. 5.2 - Find a formula for the method of moments estimate...Ch. 5.2 - Calculate the method of moments estimate for the...Ch. 5.2 - Find the method of moments estimates for and 2,...Ch. 5.2 - Use the method of moments to derive estimates for...Ch. 5.2 - Bird songs can be characterized by the number of...Ch. 5.2 - Prob. 27QCh. 5.3 - A commonly used IQ test is scaled to have a mean...Ch. 5.3 - The production of a nationally marketed detergent...Ch. 5.3 - Mercury pollution is widely recognized as a...Ch. 5.3 - A physician who has a group of thirty-eight female...Ch. 5.3 - Suppose a sample of size n is to be drawn from a...Ch. 5.3 - What confidence would be associated with each of...Ch. 5.3 - Five independent samples, each of size n, are to...Ch. 5.3 - Suppose that y1,y2,...,yn is a random sample of...Ch. 5.3 - If the standard deviation () associated with the...Ch. 5.3 - In 1927, the year he hit sixty home runs, Babe...Ch. 5.3 - A thirty-second commercial break during the...Ch. 5.3 - During one of the first beer wars in the early...Ch. 5.3 - The Pew Research Center did a survey of 2253...Ch. 5.3 - If (0.57,0.63) is a 50% confidence interval for p,...Ch. 5.3 - Suppose a coin is to be tossed n times for the...Ch. 5.3 - On the morning of November 9, 1994the day after...Ch. 5.3 - Which of the following two intervals has the...Ch. 5.3 - Prob. 18QCh. 5.3 - Prob. 19QCh. 5.3 - Prob. 20QCh. 5.3 - Prob. 21QCh. 5.3 - A public health official is planning for the...Ch. 5.3 - Prob. 23QCh. 5.3 - Given that a political poll shows that 52% of the...Ch. 5.3 - Prob. 25QCh. 5.3 - Suppose that p is to be estimated by Xn and we are...Ch. 5.3 - Let p denote the true proportion of college...Ch. 5.3 - Prob. 28QCh. 5.4 - Two chips are drawn without replacement from an...Ch. 5.4 - Suppose a random sample of size n=6 is drawn from...Ch. 5.4 - Prob. 3QCh. 5.4 - A sample of size n=16 is drawn from a normal...Ch. 5.4 - Suppose X1,X2,...,Xn is a random sample of size n...Ch. 5.4 - Prob. 6QCh. 5.4 - Let Y be the random variable described in Example...Ch. 5.4 - Suppose that 14, 10, 18, and 21 constitute a...Ch. 5.4 - A random sample of size 2, Y1 and Y2, is drawn...Ch. 5.4 - A sample of size 1 is drawn from the uniform pdf...Ch. 5.4 - Suppose that W is an unbiased estimator for . Can...Ch. 5.4 - We showed in Example 5.4.4 that 2=1ni=1n(YiY)2 is...Ch. 5.4 - As an alternative to imposing unbiasedness, an...Ch. 5.4 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.4 - An estimator n=h(W1,...,Wn) is said to be...Ch. 5.4 - Is the maximum likelihood estimator for 2 in a...Ch. 5.4 - Let X1,X2,...,Xn denote the outcomes of a series...Ch. 5.4 - Suppose that n=5 observations are taken from the...Ch. 5.4 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.4 - Given a random sample of size n from a Poisson...Ch. 5.4 - If Y1,Y2,...,Yn are random observations from a...Ch. 5.4 - Suppose that W1 is a random variable with mean ...Ch. 5.5 - Let Y1,Y2,...,Yn be a random sample from...Ch. 5.5 - Let X1,X2,...,Xn be a random sample of size n from...Ch. 5.5 - Suppose a random sample of size n is taken from a...Ch. 5.5 - Let Y1,Y2,...,Yn be a random sample from the...Ch. 5.5 - Prob. 5QCh. 5.5 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.5 - Prove the equivalence of the two forms given for...Ch. 5.6 - Let X1,X2,...,Xn be a random sample of size n from...Ch. 5.6 - Let X1,X2, and X3 be a set of three independent...Ch. 5.6 - If is sufficient for , show that any one-to-one...Ch. 5.6 - Show that 2=i=1nYi2 is sufficient for 2 if...Ch. 5.6 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.6 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.6 - Suppose a random sample of size n is drawn from...Ch. 5.6 - Suppose a random sample of size n is drawn from...Ch. 5.6 - Prob. 9QCh. 5.6 - Prob. 10QCh. 5.6 - Prob. 11QCh. 5.7 - How large a sample must be taken from a normal pdf...Ch. 5.7 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.7 - Suppose Y1,Y2,...,Yn is a random sample from the...Ch. 5.7 - An estimator n is said to be squared-error...Ch. 5.7 - Suppose n=Ymax is to be used as an estimator for...Ch. 5.7 - Prob. 6QCh. 5.8 - Prob. 1QCh. 5.8 - Find the squared-error loss [L(,)=()2] Bayes...Ch. 5.8 - Prob. 3QCh. 5.8 - Prob. 4QCh. 5.8 - Prob. 5QCh. 5.8 - Suppose that Y is a gamma random variable with...Ch. 5.8 - Prob. 7QCh. 5.8 - Find the squared-error loss Bayes estimate for in...Ch. 5.8 - Prob. 9Q
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- Given your fitted regression line, what would be the residual for snake #5 (10 C)?arrow_forwardCalculate the 95% confidence interval around your estimate of r using Fisher’s z-transformation. In your final answer, make sure to back-transform to the original units.arrow_forwardCalculate Pearson’s correlation coefficient (r) between temperature and heart rate.arrow_forward
- A researcher wishes to estimate, with 90% confidence, the population proportion of adults who support labeling legislation for genetically modified organisms (GMOs). Her estimate must be accurate within 4% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 65% of the respondents said they support labeling legislation for GMOs. (c) Compare the results from parts (a) and (b). ... (a) What is the minimum sample size needed assuming that no prior information is available? n = (Round up to the nearest whole number as needed.)arrow_forwardThe table available below shows the costs per mile (in cents) for a sample of automobiles. At a = 0.05, can you conclude that at least one mean cost per mile is different from the others? Click on the icon to view the data table. Let Hss, HMS, HLS, Hsuv and Hмy represent the mean costs per mile for small sedans, medium sedans, large sedans, SUV 4WDs, and minivans respectively. What are the hypotheses for this test? OA. Ho: Not all the means are equal. Ha Hss HMS HLS HSUV HMV B. Ho Hss HMS HLS HSUV = μMV Ha: Hss *HMS *HLS*HSUV * HMV C. Ho Hss HMS HLS HSUV =μMV = = H: Not all the means are equal. D. Ho Hss HMS HLS HSUV HMV Ha Hss HMS HLS =HSUV = HMVarrow_forwardQuestion: A company launches two different marketing campaigns to promote the same product in two different regions. After one month, the company collects the sales data (in units sold) from both regions to compare the effectiveness of the campaigns. The company wants to determine whether there is a significant difference in the mean sales between the two regions. Perform a two sample T-test You can provide your answer by inserting a text box and the answer must include: Null hypothesis, Alternative hypothesis, Show answer (output table/summary table), and Conclusion based on the P value. (2 points = 0.5 x 4 Answers) Each of these is worth 0.5 points. However, showing the calculation is must. If calculation is missing, the whole answer won't get any credit.arrow_forward
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