Question: 2. Suppose that a random variable Z has an unknown distribution with a mean of u and a variance of o. We take a

2. Suppose that a random variable Z has an unknown distribution with a mean of u and a variance of o. We take a sample of n i.i.d observations (2, 22,..., 22), calculate Zn-2 (the sample mean based on the first n-2 observations) and then construct defined by = (Zn-2) + (n-1 + n). a) Show that is an unbiased estimator of and then provide an intuitive explana- tion of why is not consistent for u. b) Find Var(), compare it with Var(Zn-2), and then discuss the efficiency of . Does attain the Cramer Rao lower bound? Briefly explain. Now let Z, Z2,... be a sequence of random variables, and suppose that for n = 1, 2, the probability distribution of Zn is given by Zn 0 n +5 Pr(Zn = Zn) 1 T c) Find an expression for E(Zn) and then briefly discuss why lim E(Zn) does not n-x exist. d) Briefly discuss why plim Zn =0. An intuitive argument is acceptable here.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a To show that is an unbiased estimator of we need to demonstrate that the expected value of equals the true population mean Lets calculate the expect... 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 Economics Questions!

10:59 First rotate the object according to the blue arrow (+90 about the y-axis), then rotate according to the red arrow (+90 about the x- axis). Use the reference dot as your...

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

A cost function is a mathematical expression of how cost drivers affect a particular cost. However, an intuitive understanding of cost functions is just as important as being able to write the...

Suppose point A is grounded (V = 0) in Figure 21-47. Find the potential at points B and C. Figure 21-47, 6.20 15 V 7.5 0 12 N 11 0

Test for exactness. If exact, solve. If not, use an integrating factor as given or obtained by inspection or by the theorems in the text. Also, if an initial condition is given, find the...

44. The number of customers entering a store on a given day is Poisson distributed with mean = 10. The amount of money spent by a customer is uniformly distributed over (0, 100). Find the mean and...

According to the Ameriprise Financial Money Across Generations study, 9 out of 10 parents with adult children ages 20 to 35 have helped their adult children with some type of financial assistance...

29. (Perpetuity) A consol is a financial security that pays in prepetuity. How much would you be willing to pay for a consol that pays $230 monthly, if the monthly interest rate is 2%?

Repeat Example 3.3, but assume that the ammonia, air, and water are brought into contact in a closed container. There is $10.0 \mathrm{~m}^{3}$ of gas space over the liquid. Assuming that the...

On January 1of the current year Aand Bform apartnership ot invest property. Acontributes investment land that she acquired two years ago, and that has an FMV of $100. As' basis ni the land at the...

TLUS (a) The truck shown in Figure 3 (a) is traveling at 90 km/h when the driver applies the brakes to come to stop. The deceleration of the truck is constant and the truck comes to a complete stop...

value; higher heating tion of a stoichiometric propane-air mixture assuming reactants at 298 K, Determine the adiabatic flame temperature for constant-pressure combus no dissociation of the products,...

Now or Never! specializes in "one day - one deal" selling. Every day they sell a product that isnot available the next day. If the item sells out, all the excess demand is lost and if items are...

Question: Transfer function of a complex control system is given below. T(s): = 30s + 3s + s s6+3s5+4s + 6s + 5s +3s+2 a) Observe system's stability according to coefficient tests and mention your...

11. [10] The stochastic exponential of a constant, that is, the process & defined by Et = exp xp (aB - 1/2), t for some constant a, is a martingale. a. Prove the above statement directly, that is, by...

As of the end of June, the job cost sheets at Racing Wheels, Inc., show the following total costs accumulated on three custom jobs Job 104 63 Job 102 Direct materials20 Job 103 Direct labor180...

Does log 81 (2401) = log 3 (7)? Verify the claim algebraically.

Let R Z+ Z+ be the relation given by the following recursive definition. 1) (1, 1) R; and 2) For all (a, b) R, the three ordered pairs (a + 1, b), (a + 1, b + 1), and (a + 1, b + 2) are also in R...

Write the dual statement for each of the following set- theoretic results. (a) (b) A = A © (A U B) (c) (d) A = (A U B) © (A U Î¸) AUB=(AnB) U (A n B) U (A n B)

a) In chess, the king can move one position in any direction. Assuming that the king is moved only in a forward manner (one position up, to the right, or diagonally northeast), along how many...

Studies by Harry Harlow showed that the most important element to developing attachment is a. feeding. b. physical contact. c. mental challenges. d. sleep.

According to Baumrind, which type of parent would most likely say, Because I said so or Its my way or the highway! a. authoritarian b. authoritative c. permissive neglectful d. permissive indulgent

According to Erikson, which stage results in a sense of independence because of ones ability to control their own actions? a. trust versus mistrust b. autonomy versus shame and doubt c. initiative...