Let X 1 ,X 2 , , X n denote a random sample from a normal distribution with mean zero and variance , 0 Show that n 1 X 2 i n is an unbiased estimator of and has variance 2 2 n

Question: Let X 1 ,X 2 , . . . , X n denote a random sample from a normal distribution with mean zero and variance

Let X₁,X₂, . . . , X_n denote a random sample from a normal distribution with mean zero and variance θ, 0 < θ < ∞. Show that Σⁿ₁ X²_i /n is an unbiased estimator of θ and has variance 2θ²/n.

Step by Step Solution

★★★★★

3.39 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Proof Let X1X2 Xn be a random sample from a normal distribution with mean 0 and ... 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 Statistical Techniques in Business Questions!

Let X 1 ,X 2 , . . . , X n denote a random sample from a Poisson distribution with mean , 0

Let X 1 ,X 2 , . . . , X n denote a random sample from a Poisson distribution with parameter , 0

\f 1 Let X 1 , X 2 ,....., X n is a random sample from a normal distribution with mean and variance 02 known. Then probabilily density function 1 x i 2 0 1 f xi 2 e , xi , 0, 0 2 By def, Likelihood...

Recall: k) In addition to many other wonderful services it provides, CourseCheggHero benets nancially from its customers' inability and/ or unwillingness to do their homework. Suppose that the time...

need full answer to attached question 3. Let X 1, X 2, . . . , X n be a random sample from a population with probability density function (26 i 1) 6 1 7 I9 fx(59;9) = (:6) 5'3 Find a Maximum...

STA5326 - Mathematical Statistics - II Homework # 3 1. If X 1 , X 2 ,..., X n is a random sample of size n from N ( , 2 ), , show that n n n 2 2 X j , X j or X , X j = = j 1 j 1 =j 1 is a sufficient...

1. Let q; > 0 be a population parameter, and let X l , X 2, , X n be a random sample from a distribution with probability density function 2 105311) : 2 9K A, , x> 0. zero otherwise. m Recall: W = X2...

Q6. Suppose that X =61 + 52, where 1 N N(6,1), 52 ~ N()\\6', A2), and 1 and 52 are in- dependent. Here, A 2 1 is a given constant, and 6 is a unknown parameter. (iv) Let X 1, X 2, - - - ,Xn be an...

Please help with this question. Please provide all steps and calculations. Please don't use answers from other websites, I looked at them and didn't understand them. Thank you Problem 7 Let X 1, X 2,...

q: I need help with question 13, the picture attached, please! tell me if the question is not clear. 13. Let (X 15, X2011, 2' = 1, . - - , n, be iid random vectors from a bivariate normal...

Company ABC has the following free cash flows to the firm (FCFF) forecast for the next 5 years: Year FCFF (in millions) Year 1 1.0 Year 2 1.2 Year 3 1.4 (All values below are in millions) Cash Debt...

Pamela Bourjaily is a consultant. Two of Pams current projects have considerable overlap, meaning that the same background research benefits both projects. The first project, from Apollo Corporation,...

P20.6 (LO 2, 3) (Lessee-Lessor Entries, Lease with a Guaranteed Residual Value) Glaus Leasing AG agrees to lease equipment to Jensen Furniture on January 1, 2025. The following information relates to...

Choose the most effective source(s) for performance information for any situation. page 367

Prove that the variance of Y can also be written Var(f) n ' (x x) i=1 n n (x x)2 i=1

Listed below are forty ordered computergenerated observations that presumably represent a normal distribution with = 5 and = 2. Can the sample be considered random with respect to the number of...

The growth of federal expenditures is one of the characteristic features of the U.S. economy. The rapidity of the increases from 2000 to 2015, as shown in the table below, suggests an exponential...

rt Two: SA Questions - (Total 3 Marks) wollat es ei oilothoq baul quorgni se to noivizoqmoo T 1. The CFA Institute divides the process of investment management into three main elements that...

What is the net present value of a project with the following cash flows if the discount rate is 11%? Year Cash Flow -$32,000 $9,000 $10,000 4 0 $15,200 $8,700 0 A. $1,332.78 OB. $1,193.77...

PROBLEM Ii-Terminology Below are isted terms and phrases commonly used in accounting Match the terms with their descriptions by placing the letter designating the term by the appropriate description...