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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Could you solve (i), (ii), (iii)? Thank you.
Consider random samples of size 258 drawn from population A with proportion 0.17 and random samples of size 310 drawn from population B with proportion 0.27. (a) Find the standard error of the distribution of differences in sample proportions, P - PB- Round your answer for the standard error to three decimal places. standard error = (b) Are the sample sizes large enough for the Central Limit Theorem to apply? OYes O No
What is the probability that a randomly selected customer will take more than 3 minutes to check out their groceries? What is P(X>3)? Round to the nearest tenths/first decimal place, 0.x
Which of the following best describes the Central Limit Theorem? (A) All of these choices are correct (B) The sample mean is close to 0.50. (C) The underlying population is normal. (D) If the distribution of a random variable is non-normal, the sampling distribution of the sample mean will be approximately normal for samples n ≥ 30.
Suppose your waiting time for a bus in the morning is uniformly distributed on [0, 10], whereas waiting time in the evening is uniformly distributed on [0, 16] independent of morning waiting time. (a) If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv's X1, , X10 and use a rule of expected value.] min (b) What is the variance of your total waiting time? (Round your answer to two decimal places.) min2 (c) What are the expected value and variance of the difference between morning and evening waiting times on a given day? (Use morning time − evening time. Round the variance to two decimal places.) expected value minvariance min2 (d) What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week? (Use morning time − evening time. Assume a week includes only Monday through…
A1. Need help plz
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.
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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