6.1.12. Let \( X_1, X_2, \ldots, X_n \) be a random sample from the Poisson distribution with \( 0 < \theta \leq 2 \). Show that the MLE of \( \theta \) is \( \hat{\theta} = \min\left\{\bar{X}, 2 \right\} \).6.1.13. Let \( X_1, X_2, \ldots, X_n \) be a random sample from a distribution with one of two pdfs. If \( \theta = 1 \), then \( f(x; \theta = 1) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2} \).

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Answered: 3, show that the mle ofis = max{0, X}.…

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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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…
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Q1: Suppose the number of customers X that enter a store between the hours 9:00 a.m. and 10:00 a.m. follows a Poisson distribution with parameter 0. Suppose a random sample of the number of customers that enter the store between 9:00 a.m. and 10:00 a.m. for 10 days results in the values 9, 7, 9, 15, 10, 13, 11, 7, 2, 12 Determine the maximum likelihood estimate of 0. Show that it is an unbiased estimator. Q2: Assume that X is a discrete random variable with pmf f(x). Let X₁,...,X₁ be a random sample on X. Suppose that the space of X is finite, say, D={a₁,...,m}. An intuitive estimate of p(a) is the relative frequency of a, in the sample. We express this more formally as follows. For j=1, 2,..., m, define the statistics 1,(X) = {1 0 X₁ = a; X₁ = a; Then the intuitive estimate of p(a)) can be expressed by the sample average p(a) = -1,(X₂) Find the unbiased estimator and the variance of the estimator and its mgf.

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3, show that the mle ofis = max{0, X}. 6.1.12. Let X₁, X2,.. Xn be a random sample from the Poisson distribution with 0 < 0 ≤ 2. Show that the mle of 0 is = min{X, 2}. ....