a) Let X₁, X₂,..., 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,lo,i) Find the conditional distribution of the likelihood function given the function of the statistic,Ô = 1 X₁. Hint: Apply f(L(0)|g(8,0)).nii) Based on i) above, is Ô = Σ₁ X¿ a sufficient statistic? Justify your answer.iii) Show whether or not >, is a consistent estimator of the parameter 1.x = 1,2,3,...elsewhere

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Answered: i) Find the conditional distribution of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The calibration of a scale is to be checked by weighing a 11 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ho: H = 11 Ha: u + 11 Ho: H + 11 H3i H 11 a (b) With the sample mean itself as the test statistic, what is the P-value when x = 10.83? (Round your answer to four decimal places.) What would you conclude at significance level 0.01? Conclude that the true mean measured weight differs from 11 kg. Conclude that the true mean measured weight is the same as 11 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 11.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 10.9? (Round your answer to…
The number of people who dine at restaurants in Buffalo is normally distributed with a µ = 30 people and = 3 people. (Report both the z-scores and probability) What is the probability that the mean of 7 restaurants will have between 21 and 32 people dining there? z1 = z2 = p(21 > M > 32) = What is the probability that the mean of 13 restaurants will have less than 21 people dining there? z = p(M < 21)= Is the p=0 when the z score is extreme like -10 or 10?
SAT scores in one state is normally distributed with a mean of 1532 and a standard deviation of 200. Suppose we randomly pick 50 SAT scores from that state. a) Find the probability that one of the scores in the sample is less than 1492. P(X < 1492) = b) Find the probability that the average of the scores for the sample of 50 scores is less than 1492. P(X < 1492) = Round each answer to at least 4 decimal places.
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Please show work on paper please
Please do question 2e and 2f with full handwritten working out
t3 solve both please
The average wait time to get seated at a popular restaurant in the city on a Friday night is 12 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 13 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 13, 13, 11, 13, 13, 13, 13, 10, 12, 13, 13, 10, 13 What can be concluded at the the αα = 0.05 level of significance level of significance? The null and alternative hypotheses would be: H0 = (p,u) (<,>,=,not equal) to _____ H1 = (p,u) (<,>,=,not equal) to _____ The test statistic (t,z) = ___ The p-value = _____ Thus, the final conclusion is that ... The data suggest that the population mean wait time for men who wear a tie is not significantly more than 12 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 12. The data suggest the population mean is not significantly more than 12…
6. Interval estimation when o is unknown (the data “Alcohol" is provided) Consumption of alcoholic beverages by young women of drinking age has been increas- ing in the United Kingdom, the United States, and Europe (The Wall Street Journal, Feb- ruary 15, 2006). Data (annual consumption in liters) consistent with the findings reported in The Wall Street Journal article are shown for a sample of 20 European young women. 266 82 199 174 97 170 222 115 130 169 164 102 113 171 93 93 110 130 Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean annual consumption of alcoholic beverages by European young women.
Current Attempt in Progress State the null and alternative hypotheses for the situation described below for a statistical test. Testing to see if there is evidence that the proportion of people who smoke is greater for males than for females. Let group 1 be the males and let group 2 be the females. Ho: = < vs Ha: 41 :: p 2 :: p ^ P₁ P1 ^ :: P2 P2 p I ₁ :: I₂
Parametric Confidence Interval
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