Question: Let X1, X2,..., Xn are random samples from geometric distribution with the probability density function f(x|0) = (1 - 0)*-10, for x = 1,2,3,... with

Let X1, X2,..., Xn are random samples from geometric distribution with the probability density function f(x|0) = (1 - 0)*-10, for x = 1,2,3,... with 0ol are parameters. Given E[X] =

a) Find the moment estimator for θ.

b) Provide a definition of a maximum likelihood estimator. Next, find the maximum likelihood estimator for θ.

c) If θ1, and θ2, are both fair estimators of θ, explain how the efficiency of the estimator can be measured and used to compare the two estimators.

d) Explain how to determine whether an estimator is a minimum variance unbiased estimator.

Step by Step Solution

★★★★★

3.45 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ANSWER a The moment estimator for is 1x b A maximum likelihood estimator is an estimator that max... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

The probability density function of the random variable X is given by Find the expected value of the random variable X. 0

The probability density function for an exponential distribution is ex where x is the value of the variable and is a parameter. The cumulative probability distribution is 1 ex. Suppose that two...

The probability density function of a random variable X is given by (a) Find c. (b) Find the distribution function F(x). (c) Compute P (1 cx, 0

The I.Q.s of 10 teenagers belonging to one ethnic group are 98, 114, 105, 101, 123, 117, 106, 92, 110, and 108, whereas those of 6 teenagers belonging to another ethnic group are 122, 105, 99, 126,...

Let X 1 , . . . , X n be a simple random sample from a N(Î¼, Ï 2 ) population. For any constant k > 0, define Consider ÏÌ 2 k as an estimator of Ï 2 . a. Compute...

Suppose that three random variables X1, X2, and X3 have a continuous joint distribution with the following joint p.d.f.: f (x1, x2, x3) = Determine (a) The value of the constant c. (b) The marginal...

Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles. Let X represent the diameter, in micrometers, of a randomly chosen...

The steps in this exercise lead to the probability density function of an Erlang random variable X with parameters and r, f(x) = r xr1 e /(r 1) !, x > 0, r = 1, 2, . .. (a) Use the Poisson...

Use the information given in question 7 to find P(3 X 7). Question 7 Suppose a random variable X can take on only values in the range from 2 to 10 and that the probability that the variable will...

Silver Springs Moving and Storage Inc. is studying the relationship between the number of rooms in a move and the number of labor hours required for the move. As part of the analysis, the CFO of...

Q.15 The sum of the infinite series 7-1 n 3" is (Correct upto two decimal places)__

The following events apply to Gulf Seafood for the 2016 fiscal year: 1. The company started when it acquired $60,000 cash by issuing common stock. 2. Purchased a new cooktop that cost $40,000 cash....

Evaluate s i n 4 x d x 3 8 x - 1 4 s i n ( 2 x ) 1 3 2 s i n ( 4 x ) C 3 8 x 1 4 s i n ( 2 x ) - 1 3 2 s i n ( 4 x ) C 3 2 x s i n ( 2 x ) - 1 8 s i n ( 4 x ) C 3 8 x - 7 3 2 s i n ( 2 x ) C

The 1650-kg car has its mass center at G. Calculate the normal forces NA and NB between the road and the front and rear pairs of wheels under conditions of maximum acceleration. The mass of the...

Computer mediated communication (CMC) is a form of interaction that heavily involves technology (e.g., instant messaging, email). A study was conducted to compare relational intimacy in people...

Sketch the Nyquist diagram for each of the systems in Figure P10.1. R(s) + E(s) 50 C(s) s(s + 3)(s + 6) System I R(s) + 50 C(s) s2(5 + 1) (s+ 4) System 2 R(s) + 20 C(s) s(s + 1) (s +3) (s+ 4) System...

A certain parachute has a drag coefficient of C D = 1.5. If the parachute and skydiver together weigh 225 lb, what should the frontal area of the parachute be so that the skydivers terminal velocity...

Read the definition of a 2DFA (two-headed finite automaton) given in Problem 5.26. Prove that P contains a language that is not recognizable by a 2DFA. Problem 5.26. Define a two-headed finite...

The sum of my number and two and two thirds is seven. What is my number? 7 is in one box. Below it are 2 boxes. N is in one. 2 and 2-thirds is in the other. Check all that apply. The variable, n,...

Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all 10! possible rankings are equally likely. Let X denote the highest ranking...

Two points are selected randomly on a line of length L so as to be on opposite sides of the midpoint of the line. [In other words, the two points X and Y are independent random variables such that X...

If X1, X2, . . . ,Xn are independent and identically distributed random variables having uniform distributions over (0, 1), find (a) E[max(X1, . . . ,Xn)]; (b) E[min(X1, . . . ,Xn)].

Suppose the phase I sample is an unequal-probability sample of observations. If we observed yi for every unit in S (1), we could use the Horvitz Thompson estimator of the variance of the...

This exercise is based on results in McNamee (2003) on the use of two-phase sampling to estimate disease prevalence. An inexpensive, but possibly inaccurate, screening test for the disease is given...

Optimal allocation for two-phase sampling with stratification. Suppose phase I is an SRS and phase II is a stratified random sample, and that the total cost for the sample is given in (12.15), where...