Question: If X1 and X2 are independent random variables having binomial distributions with the parameters and n1 and and n2, show that X1 +

If X1 and X2 are independent random variables having binomial distributions with the parameters θ and n1 and θ and n2, show that X1 + X2 / n1 + n2 is a sufficient estimator of θ.

Step by Step Solution

★★★★★

3.50 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

by theorem estimato... 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)

583-M-S-P-E (794).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

If X1 and X2 are independent random variables having exponential densities with the parameters 1 and 2, use the distribution function technique to find the probability density of Y = X1 + X2 when (a)...

If X1 and X2 are independent random variables having the geometric distribution with the parameter , show that Y = X1 + X2 is a random variable having the negative binomial distribution with the...

Suppose that X1 and X2 are independent random variables and that Xi has the Poisson distribution with mean i (i = 1, 2). For each fixed value of k (k = 1, 2, . . .), determine the conditional...

If X1 and X2 are independent random variables having binomial distributions with the respective parameters n1 and and n2 and , show that Y = X1 + X2 has the binomial distribution with the parameters...

Use the moment-generating function technique to rework Exercise 7.27. In exercise If X1 and X2 are independent random variables having binomial distributions with the respective parameters n1 and ...

17. Test of the Equality of Proportions. Let X1 and X2 be independent random variables with Binomial distributions Binomial(ni, pi), i 1,2, where the nis are assumed known. Consider testing the null...

Suppose that X1 and X2 are independent random variables, that X1 has the binomial distribution with parameters n1 and p, and that X2 has the binomial distribution with parameters n2 and p, where p is...

7.27. If X1 and X2 are independent random variables hav- ing binomial distributions with the respective parameters n1 and 0 and n2 and 0, show that Y = X1 + X2 has the binomial distribution with the...

9.1.4 Assume that X1 and X Z are independent random variables, with binomial distributions with parameters n1, p and n2, p respectively. Find a correlation coefficient between XI and X1 + XZ.

Answer each question and label them with their corresponding letter or number. Show work. 1 2. The lifetime in years of a manufactured product is Y = 5X^0.7, where X has an exponential distribution...

Repeat Problem 43, but replacing the 10 Mbps link with a 10 Gbps link. Note that in your answer to part c, you will realize that it takes a very long time for the congestion window size to reach its...

Exacto Company reported the following net income and dividends for the years indicated: True Corporation acquired 75 percent of Exacto's common stock on January 1, 20X5. On that date, the fair value...

A a... e Evolve End-of-Life Decision... Report co Question 50 of 50 The nurse is gathering data from a non-English-speaking patient through the use of an interpreter. Which action would the nurse...

Describe the major characteristics of the management philosophy of the South Korean Chaebol Samsung and the culturally based strengths and weaknesses in terms of developing the business.

The following table lists the number of firms where the top executive officer made over $1 million per year. The table also lists firms according to whether shareholder return was positive during the...

According to USA Today, 65% of Americans are overweight or obese. If five Americans are chosen at random, what is the probability that at least one of them is overweight or obese?

The chancellor of a state university is applying for a new position. At a certain point in his application process, he is being considered by seven universities. At three of the seven he is a...

Which of the following accounts increases with a debit ? a) Interest Payable b) Accounts Payable c) Cash d) Capital

Lockheed Corporation purchased a machine on January 2, 2020, for $4,000,000. The machine has an estimated 5-year life with no salvage value. The straight-line method of depreciation is being used for...

Asset W has an expected return of 10.6 percent and a beta of 1.40. If the risk-free rate is 3.6 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Leave no cells...