Let X₁, X₂, ...,2, ..., Xn be a random sample of size n from population X. Suppose that X has thefollowing probability mass function:f(x; 0) = (0 (1 - 0)x-1,(0,i) Find the conditional distribution of the likelihood function given the function of the statistic,nÔ = ₁X₁. Hint: Apply f(L(0)|g(,0)).ii) Based on i) above, is =iii) Show whether or not >, is a consistent estimator of the parameter 1.x = 1,2,3,...elsewhere₁X₁ a sufficient statistic? Justify your answer.=1

Answered: Image /qna-images/answer/5756e6b8-ec5f-47cb-87c2-0c390ed04b9e.jpg

Answered: i) Find the conditional distribution of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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SAT scores in one state is normally distributed with a mean of 1526 and a standard deviation of 112. Suppose we randomly pick 46 SAT scores from that state.a) Find the probability that one of the scores in the sample is less than 1529.P(X<1529)P(X<1529) = b) Find the probability that the average of the scores for the sample of 46 scores is less than 1529.P(¯¯¯X<1529)P(X¯<1529) =
Assume that we want to construct a confidence interval. Which letter is correct? The confidence level is 99%, σ=3624 thousand dollars, and the histogram of 60 player salaries (in thousands of dollars) of footbal players on a team is as shown. a) find the critical value tα/2 b) find the critical value zα/2 c) neither the normal distribution nor the t distribution applies.
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Heart rates are determined before and 30 minutes after a Kettleball workout. It can be assumed that heart rates (bpm) are normally distributed. Use the data provided below to test to determine if average heart rates prior to the workout are significantly lower than 30 minutes after a Kettleball workout at the 0.02 level of significance. Let μ₁ = mean before workout. Select the correct Hypotheses: Ho:με 2 με Η: μι = με Η: μη μ₂ O O O Conclusion: before 69 69 65 62 63 61 after 73 75 72 70 68 59 O Fail to Reject Ho ● Reject Ho Test Statistic = p-value = Ho:μd = 0 H₁: Hd ‡0 O [three decimal accuracy] [three decimal accuracy] Ho:μα 20 Ha:Pa 0 O Interpret the conclusion in context: ● There is enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout. O There is not enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout.
Construct a 95% confidence interval to estimate the population mean using the data below. x=38 s=11 n=39 With 95% confidence, when n=39 the population mean is between a lower limit of and an upper limit of (Round to two decimal places as needed.)
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11
Let the test statistic T have at distribution when H, is true. Give the P-value for each of the following situations. (Round your answers to three decimal places.) n USE SALT (a) H: u > Ho, df = 13, t = 2.663 P-value = (b) H3: µ < Ho, n = 27, t = 2.131 P-value = (c) H: u # Ho, n = 41, t = -1.581 or t = 1.581 P-value =
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i) Find the conditional distribution of the likelihood function given the function of the statistic, Ô = ₁ X₁. Hint: Apply f(L(0)|g(,0)). ii) Based on i) above, is = ii) Show whether or not X, is a consistent estimator of the parameter 1 X₁ a sufficient statistic? Justify your answer.