Let X1,..., Xn be a random sample (i.i.d.) following Gamma(2, 3) for some unknown pa-rameter 3 > 0.(а)What is the MLE of 3? Derive it.Is the MLE of Ba consistent estimator for 3? Prove/disprove it.(b)Hint: You may need continuous mapping theorem for convergence in probability.(c) (What is the Method of Moments estimator of 3?(d)Gamma(a, b)Now let's think like a Bayesian. Consider a prior distribution of 3for some a, b > 0. Derive the posterior distribution of 3 given (X1, .Hint: For Gamma likelihood with known a (= 2) and unknown 3 (as is our case), theX„) = (x1,. .. , xn).....conjugate prior on 3 is a Gamma distribution.(e)of 3 assuming squared error loss?Using the same prior as in the previous sub-question, what is the Bayes estimator

Answered: Let X1,..., X, be a random sample…

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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An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given. y p(y) 0 1 0.50 0.35 0.10 0.05 USE SALT 3 (a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.) (b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ≤ x ≤ b). Round your answer to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.
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Suppose that we want to use the normal approximation to the binomial distribution to determine b(1; 150, 0.05). (a) Based on the rule of thumb on page 192 (A good rule of thumb is to use this approximation only when nθ and n(1 − θ) are both greater than 5), would we be justified in using the approximation? (b) Make the approximation and round to four decimals. (c) If a computer printout shows that b(1; 150, 0.05) = 0.0036 rounded to four decimals, what is the percentage error of the approximation obtained in part (b)?

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