# Question: If X1 X2 Xn constitute a

If X1, X2, . . . , Xn constitute a random sample of size n from an exponential population, show that is a sufficient estimator of the parameter θ.

## Relevant Questions

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. If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + · · · + Xn is a sufficient estimator of the parameter θ. Use the method of maximum likelihood to rework Exercise 10.53. In exercise Given a random sample of size n from a Poisson population, use the method of moments to obtain an estimator for the parameter λ. Use the method of maximum likelihood to rework Exercise 10.56. In exercise If X1, X2, . . . , Xn constitute a random sample of size n from a population given by Find estimators for ∂ and θ by the method of moments. This ...Making use of the results of Exercise 6.29 on page 184, show that the mean of the posterior distribution of Θ given on page 304 can be written as That is, as a weighted mean of x/n and θ0, where θ0 and σ20 are the mean ...Post your question