Let X 1 ,X 2 , ,X n be a random sample from the Poisson distribution with 0 2 Show that the mle of is min X, 2 ...

Let X 1 ,X 2 , . . .,X n be a random sample from the Poisson

Question:

Let X₁,X₂, . . .,X_n be a random sample from the Poisson distribution with 0 < θ ≤ 2. Show that the mle of θ is ^{^}θ = min{‾X, 2}.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

See More Books

Question Posted: Oct 14, 2022 03:03 AM

See More Questions

Let X1,..., Xn be a random sample from the pdf f(x|) = e-(x-) where - < < x < . a. Show that X(1) = mini Xi is a complete sufficient statistic. b. Use Basu's Theorem to show that X(1) and S2 are...
Let X1,..., Xn be a random sample from the pdf f(x|) = x-2, 0 < < x < . a. What is a sufficient statistic for ? b. Find the MLE of . c. Find the method of moment's estimator of .
Let X1, X2,..., Xn be a random sample from a uniform distribution on the interval [0, Ã¸], so that Then if Y = max (Xi), it can be shown that the rv U = Y/Ã¸ has density...
The common stock of Fido Corporation was trading at $45 per share on October 15, 2010. A year later, on October 15, 2011, it was trading at $80 per share. On this date, Fidos board of directors...
Griffin Company, an IFRS reporter, holds a held- to-maturity investment at amortized cost of $ 250,000. The debt investment is classified as held- to- maturity. The cur-rent fair value of the The...
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. Table 1 f(x) = arctan(x 2 ) 1 2x" = 1 + x + x? + x + ... R = 1 n=0 00 x" e* = E- n=0 n! 1 + 1! R = 0 2! + 3!...
Fraud deterrence is centered on the fear of getting caught and the fear of getting punished. In your opinion, which is stronger and why?
The Colson Company issued $300,000 of 10% bonds on January 1, 2011. The bonds are due January 1, 2016, with interest payable each July 1 and January 1. The bonds are issued at face value. Prepare...
Identify and analyze at least two considerations to ensure effective transaction transparency of Centralized database management systems and Distributed Database management systems. Identify...
Prove, or find a counterexample to, each of the following assertions: a. If or |= (or both) then ( ) b. If ( ) then and . c. If ( ) then or (or both).
Let X 1 ,X 2 , . . .,X n be a random sample from a distribution with pdf f(x; ) = exp{|x|} /2(1/), < x < , where > 0. Suppose = { : = 1, 2}. Consider the hypotheses H 0 : = 2 (a normal...
Let X 1 ,X 2 , . . . , X n be a random sample from a ( = 3, = ) distribution, where 0 < < . (a) Show that the likelihood ratio test of H 0 : = 0 versus H 1 : 0 is based upon the statistic W = ...
State the type of expenditure, capital or revenue, incurred in the following transactions (a) Break-down van purchased by a garage. (b) Repairs to a fruiterers van. (c) The cost of installing a new...
A colony of bacteria has a doubling time of 5.23 hours. - If there are 7830 bacteria in the colony at 9:00 am, how many are there at noon the next day?Enter only the number, rounded to the nearest...
I5 Assignment 6 This assignment relates to your first written essay (of 3). We are now moving into the third section of the class in which we will focus on the spending or the expenditure components...
How is ECEF speed calculated? The expected baseline for calculating ECEF velocities is the discrete Position/Time between consecutive points. The velocity at the first input point is defined as 0....
A theater has 44 seats in the first row, 48 seats in the second row, 52 seats in the third row, and so on. (A) Can the number of seats in each row be represented by an arithmetic or geometric...
When a cannonball is fired, the equation of its trajectory can be represented by h(t)=16t^2+123t where h(t) represents the height in feet after tt seconds. a) Find the maximum height of the...
The Radisson Diamond uses pontoons and stabilizers to damp out the effect of waves hitting the ship. The block diagram of the ship's roll control system is shown. Determine the feedback gains K2 and...
Differentiate. y = ln(3x + 1) ln(5x + 1)
Let X 1 , X 2 , . . . , X n denote the outcomes of a series of n independent trials, where for i =1, 2, . . . , n. Let X = X 1 + X 2 + + X n . (a) Show that p 1 = X 1 and p 2 = X/n are unbiased...
Suppose that n = 5 observations are taken from the uniform pdf, fY (y; ) = 1/, 0 y , where is unknown. Two unbiased estimators for are 1 = 6/5Y max and 2 = 6Y min Which estimator would be...
Let Y 1 , Y 2 , . . . , Y n be a random sample of size n from the pdf f Y (y; ) = 1 e y/ , y > 0. (a) Show that 1 = Y 1 , 2 = Y, and 3 = n Y min are all unbiased estimators for . (b) Find the...
O. A seller wanted to net $20,000 on the sale of property. The seller had a first mortgage on the property of $61,800. The broker charged a 7% commission with the seller also having to pay $2,000 in...
PSA 9-4 Determine the Cost of Goods Sold and the Merchandise Inventory Balance #1 Metalworks Inc. sells office furniture to corporate customers. The company uses the perpetual inventory system and...
Western Services has three service departments: Information Systems (IS), Personnel, and Administration. There are two operating departments: Residential and Commercial. A summary of costs and other...

Let X 1 ,X 2 , . . .,X n be a random sample from the Poisson

Question:

Step by Step Answer:

In order to find the ...View the full answer

Introduction To Mathematical Statistics

Students also viewed these Business questions