Let X1, , Xn be iid with geometric distribution P(X x) (1 )x 1, x 1, 2, , 0 1 Show that Xi is sufficient for , and find the family of distributions of Xi Is the family complete

Question: Let X1,..., Xn be iid with geometric distribution P(X = x) = (1 - )x-1, x = 1, 2,..., 0 < < 1. Show

Let X1,..., Xn be iid with geometric = x) = θ(1 - θ)x-1, x = 1, 2,..., 0 < θ < 1.
Show that ∑Xi is sufficient for θ, and find the family of distributions of ∑Xi. Is the family complete?

Step by Step Solution

★★★★★

3.36 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The population pmf is f x 1 x1 1 e log ... 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

Document Format (1 attachment)

941-M-S-P (8731).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

What is an organization and what characteristics do organizations share?

Let X1, . . ., Xn be a random sample of size n from the geometric distribution for which p is the probability of success. (a) Use the method of moments to find a point estimator for p. (b) Use the...

As a generalization of the previous exercise, let X1,... ,Xn be iid with pdf Let X(1) a-1 otherwise

Let X1,..., Xn be iid with pdf fx(x), and let X denote the sample mean. Show that fx(x) = nfXl +.....+ xn(nx),

Let X1, . . . , Xn be i.i.d. from Uniform distribution on the interval (1, 1 + 2), where 1 R, 2 > 0. both 1 , 2 unknown. Find UMVUE of 2, by proving unbiased statistics or conditional expectation....

Boos and Hughes-Oliver (1998) detail a number of instances where application of Basu's Theorem can simplify calculations. Here are a few. a. Let X1,..., Xn be iid n(Î¼, Ï2), where...

STATISTICS 251 HOMEWORK ASSIGNMENT 8 DUE FRIDAY NOV 18 Problem 1. Let U1 , U2 be independent uniform random variables on [0, 1], and write M = max(U1 , U2 ). (a) Find the conditional joint density of...

2.25 Suppose that X1, . . . , Xn are i.i.d. with the pdf f (x) = 1 cos(x) x2 ,

4. (a) Generate data by drawing a sample of size n = 30 from N(f.J, 1) with f.1 = 2. For your data, plot the likelihood function and comment on its shape and how informative it is about f.J. (b) For...

Stat question : (x+0)2 Problem 2. Let X1, ..., Xn be i.i.d. random variables with density f (x) = 1 V2IT e 2 . Consider the test Ho: 0 = 0 versus H1:0 = 1. a. Find a test statistic and the form of...

Question 6*: Let X1, . . . an be iid normal with mean p: and variance 1. a. Obtain the distribution of T = (X1 M2 + . . . + (Xn M2. 13. Derive the moment generating function of T

Q1 The text discusses a study that says our moods actually get worse when we spend a lot of time on Facebook or snapchat or TikTok because we feel like were wasting our time. Even Facebook...

A mass of 15 kg of air in a piston - cylinder device is heated from 25 to 77oC by passing current through a resistance heater inside the cylinder. The pressure inside the cylinder is held constant at...

P10.18 NASA is developing remote manipulators that can be used to extend the hand and the power of hu mankind through space by means of radio. A concept of a remote manipulator is shown in Figure...

Capital Budgeting XYZ enterprise currently issues bond of $5 million with 10% interest rate. XYZ plans to issue $1 million more bonds at the end of each year for the next 5 years. If XYZs marginal...

Cost of raw materials is debited to Raw Materials Inventory when the A. Materials are put into production. B. Bill for the materials is paid. C. Materials are ordered. D. Materials are received.

need a review on this article https://www.scientificamerican.com/article/can-algae-feed-the-world-and-fuel-the-planet/

Below i attached all the URL links Click those and take help from them to create a power point presentation and upload here in the image formet then i will create a power point file do not copy and...

PL) Determine the Forces in the members of Hhe inbenally vealundant truss Shown in E = 29,000 Ksi 2uft 24Pt1 24ft 2iu2 2. Liuz 24 ft 2inz 2inz 2 iuz 2 juz lok 25 K 2 in?

You are managing a project with team members located at customer sites on three different continents. You have a number of stakeholders on your project, and most of them are located outside of the...

Why do we care about probabilistic inequalities?

Explain the concepts of a percentile and a quantile and how they are related.

Compare and contrast the cumulative distribution function and the quantile function.

Indicate whether each of the following would be in the section of financial statements identified as a) current asset b) property, plant, and equipment c) current liability d)revenue or e) expense 1....

What is the realized return percent? The following table contains prices and dividends for a stock. All prices are after the dividend has been paid. If you bought the stock on January 1 and sold it...

A terminated employee is not entitled to COBRA benefits if he is terminated for gross misconduct. Group of answer choices True False