4. [Limit Theorems] Suppose there is a random sample of n calendar days and for each day we observe the number of purchase orders recieved by an online market, {x1, x2, , ..., xn}. Assume that the number of orders follows the Poisson distribution with the daily intensity parameter A. (a) Suggest a consistent estimator  for the unobserved parameter A. (b) Using the Central Limit Theorem, derive the asymptotic distribution of  as n → ∞o. (c) Can you suggest a transformation g(Â) for this estimator such that the asymptotic distribution does not depend on the latent parameter \?
4. [Limit Theorems] Suppose there is a random sample of n calendar days and for each day we observe the number of purchase orders recieved by an online market, {x1, x2, , ..., xn}. Assume that the number of orders follows the Poisson distribution with the daily intensity parameter A. (a) Suggest a consistent estimator  for the unobserved parameter A. (b) Using the Central Limit Theorem, derive the asymptotic distribution of  as n → ∞o. (c) Can you suggest a transformation g(Â) for this estimator such that the asymptotic distribution does not depend on the latent parameter \?
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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![4. [Limit Theorems] Suppose there is a random sample of n calendar days and for each day we observe
the number of purchase orders recieved by an online market, {x1, x2, , ..., xn}. Assume that the number
of orders follows the Poisson distribution with the daily intensity parameter A.
(a) Suggest a consistent estimator  for the unobserved parameter A.
(b) Using the Central Limit Theorem, derive the asymptotic distribution of  as n → ∞o.
(c) Can you suggest a transformation g(Â) for this estimator such that the asymptotic distribution
does not depend on the latent parameter \?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3b25b0a-ae43-4671-b334-ec72999c55c5%2F744a36d1-4020-48a1-872b-d5a886a29cde%2Frh37vnb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. [Limit Theorems] Suppose there is a random sample of n calendar days and for each day we observe
the number of purchase orders recieved by an online market, {x1, x2, , ..., xn}. Assume that the number
of orders follows the Poisson distribution with the daily intensity parameter A.
(a) Suggest a consistent estimator  for the unobserved parameter A.
(b) Using the Central Limit Theorem, derive the asymptotic distribution of  as n → ∞o.
(c) Can you suggest a transformation g(Â) for this estimator such that the asymptotic distribution
does not depend on the latent parameter \?
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