3. (Problem 10.41 of Freund's) To show that an estimator can be consistent with-out being unbiased nor asymptotically unbiased, consider the following estimationprocedure. Let X₁,..., Xn be a random sample from a population with mean μand finite variance o2. Consider the following estimation procedure: First, we ran-domly draw one slip of n papers numbered from 1 to n. If we get 2,3,...,n, we-1 nuse X = n ¹₁ as our estimate for u; otherwise, we use n² as the estimate fori=1μ. Show that this estimation procedure is(a) consistent.(b) neither unbiased nor asymptotically unbiased.

From the above given data the following solution is provided below:

Answered: 3. (Problem 10.41 of Freund's) To show…

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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1) Suppose tha Y is a random variable having an gamma distribution with a = 1, find the value of k such that an interval from 0 to ky is a (1 - a) 100% confidence interval for the parameter B.
15. The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 10.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eightfull-time faculty for one week is shown in the table below. At α=0.05, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 11.2 7.5 12.2 7.2 4.1 9.5 13.7 8.5 Question content area bottom Part 1 (a) Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha? A. H0: μ>10.0 Ha: μ≤10.0 B. H0: μ≠10.0 Ha: μ=10.0 C. H0: μ<10.0 Ha: μ≥10.0 D. H0: μ≤10.0 Ha: μ>10.0 E. H0: μ≥10.0 Ha: μ<10.0
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e 14-25. A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1-5. Calculate the proportion of days on which (i) Neither car is used (ii) Some demand is refused.
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