Question: 7.5.10. Let $X_{1}, X_{2}, ldots, X_{n}$ be a random sample from a distribution with pdf $f(x ; theta)=theta^{2} x e^{-theta x], 0 0 .$ (a)

$7.5.10. Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from$

7.5.10. Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from a distribution with pdf $f(x ; \theta)=\theta^{2} x e^{-\theta x], 00 .$ (a) Argue that $Y=\sum_{1}^{n} X_{i}$ is a complete sufficient statistic for $\theta$. (b) Compute $E(1 / Y$ and find the function of $y$ that is the unique MVUE of $\theta$. SP.PB. 107

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

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 Databases Questions!

7.5.10. Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from a distribution with pdf $f(x; \theta)=\theta^{2} x e^{-\theta x}, 0 0 .$ (a) Argue that $Y=\sum_{1}^{n} X_{i}$ is a complete...

2. (a) Consider $X_{1}, X_{2}, \ldots, X_{m}$ be a random sample from the Normal $\left(\mu_{1}, \sigma^{2} ight) $ distribution and $Y_{1}, Y_{2}, \ldots, Y_{n}$ be a random sample from the Normal...

Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from a normal population with zero mean and unknown variance $\sigma^{2}$. Find the maximum likelihood estimator of $\sigma^{2}$. [8] Let...

data c140 ## 1. Prediction with Sums Let $X_1, X_2, \ldots, X_n$ be i.i.d. with expectation $\mu$ and variance $\sigma^2$. Let $S = \sum_{i=1}^n X_i$. **a)** Find the least squares predictor of $S$...

Refer to Exercise 6.40. Let $X_{1}, X_{2}, \ldots, X_{n}$ be $n$ independent random variables each having a negative binomial distribution with success probability $p$ but where $X_{i}$ has...

Let $X_{1}, X_{2}, \ldots$ be independent and identically distributed random variables with $E\left[X_{i}ight]=0$, and let \[S_{n}=\sum_{i=1}^{n} X_{i}\] Show that $S_{1}, S_{2}, \ldots$ form a...

Let $X_{1}, X_{2}, \ldots$ be a sequence of i.i.d. observations from discrete uniform $(1,2, \ldots, \theta $ distribution for some integer $\theta>1$. a) Show that $2 \bar{X}_{n}-1$ is a consistent...

Let $X_{1}, X_{2}, \ldots, X_{20}$ be independent and let each have the same marginal distribution with mean 10 and variance 3. Find (a) $E\left(X_{1}+X_{2}+\cdots+X_{20} ight)$; (b)...

Let $X_{1}, X_{2}, \ldots, X_{50}$ be independent and let each have the same marginal distribution with mean -5 and variance 8 . Find (a) $E\left(X_{1}+X_{2}+\cdots+X_{50} ight)$; (b)...

What is the meaning of risk management?

What is the z-value for a one-tail (upper) probability of 5%?

The president of ABC Inc, notifies the TSX at ncon today that it is meeting with its credinors at 1 : 0 0 PM ( EST ) Fis ahemoon to determine whether they wa accept a debt reorganization plan. What...

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

LO2 Identify components of workflow analysis.

1. The development of important skills in employees is always a concern for human resource professionals and managers. Skills gaps continue to challenge organizations, and proper steps need to be...

4. Job analysis enables human resource professionals and operating managers to identify the proper tasks, duties, and responsibilities of various organizational jobs. Given its importance, the...