Let X1,..., Xn and Yi,..., Ym be two independent samples from a Poisson dis- tribution with...

Question

Question

Let X1,..., Xn and Yi,..., Ym be two independent samples from a Poisson dis- tribution with parameter X. Let a, b be two posi

Answer 1

Answer #1

Let X, X.. Xom and Y. 7. Im ~P(d) Then E(X) = E(Y) = 2 & ij. Y + 2 + tlm het i = a X, + X 2 + + xn n m 1 W E()) = 2 E(X + X 2

Answer 2

Similar Homework Help Questions

Let X1, ..., Xn and Y1, ...,Ym be two independent samples from a Poisson dis- tribution...

Let X1, ..., Xn and Y1, ...,Ym be two independent samples from a Poisson dis- tribution with parameter 1. Let a,b be two positive numbers. Consider the following estimator for 1: i-X1 + ... + Xn+hY1 + ... + Ym m п (a) What condition is needed on a and b so that û is unbiased? (b) What is the MSE of Î?
Let X1, ..., Xn and Y1, ..., Ym be two independent samples from a Poisson dis-...

Let X1, ..., Xn and Y1, ..., Ym be two independent samples from a Poisson dis- tribution with parameter 1. Let a, b be two positive numbers. Consider the following estimator for 1: i ,Y1 +...+Ym = a- X1 +...+Xn n т (a) What condition is needed on a and b so that û is unbiased? (b) What is the MSE of i?
Given two independent random samples X1, ..., Xn and Y1, ..., Ym with normal dis- tributions...

Given two independent random samples X1, ..., Xn and Y1, ..., Ym with normal dis- tributions N(Hz, o?) and N(Hy, oz), determine a generalized likelihood ratio test for Ho : Mix - My = 0 versus H : plz – My 70 at a given significance level a (01, 0y unknown but equal).

3. Let X1, X2, . . . , Xn be independent samples of a random variable...

3. Let X1, X2, . . . , Xn be independent samples of a random variable with the probability density function (PDF): fX(x) = θ(x − 1/ 2 ) + 1, 0 ≤ x ≤ 1 ,0 otherwise where θ ∈ [−2, 2] is an unknown parameter. We define the estimator ˆθn = 12X − 6 to estimate θ. (a) Is ˆθn an unbiased estimator of θ? (b) Is ˆθn a consistent estimator of θ? (c) Find the mean squared...
Let X1, . . . , Xn be independent Poisson(θ) random variables with parameter θ >...

Let X1, . . . , Xn be independent Poisson(θ) random variables with parameter θ > 0. (1) Find the Bayes estimator of θ for a Gamma(α, β) prior. (2) Find the MSE of the Bayes estimator.
In 10. 11, Let X1, X2, . , Xn and Yi, Y2, . . . , Y,, be independent samples from N(μ, σ?) and N(...

In 10. 11, Let X1, X2, . , Xn and Yi, Y2, . . . , Y,, be independent samples from N(μ, σ?) and N(μ, σ), respectively, where μ, σ. ơỈ are unknown. Let ρ-r/of and g m/n, and consider the problem of unbiased estimation of u In 10. 11, Let X1, X2, . , Xn and Yi, Y2, . . . , Y,, be independent samples from N(μ, σ?) and N(μ, σ), respectively, where μ, σ. ơỈ are unknown....

Let X1, X2,..., Xn be a random sample from Poisson(0), 0 > 0. X. Determine the...

Let X1, X2,..., Xn be a random sample from Poisson(0), 0 > 0. X. Determine the value of a constant c such that the (b) Let Y =1 -0 unbiased estimator of e. estimator eCYis an (c) Get the lower bound for the variance of the unbiased estimator found in (b) Let X1, X2,..., Xn be a random sample from Poisson(0), 0 > 0. X. Determine the value of a constant c such that the (b) Let Y =1 -0...
Suppose X1,. , Xn are iid Poisson(A) random variables. Show by direct calculation without using any...

Suppose X1,. , Xn are iid Poisson(A) random variables. Show by direct calculation without using any theoremm in mathematical statistics, that (a) Ση! Xi/n is an unbiased estimator for λ. (b) X is optimal in MSE among all unbiased estimators. This is to say, let T be another unbiased estimator, then EA(X) EA(T2
Q3 Suppose X1, X2, ..., Xn are i.i.d. Poisson random variables with expected value ). It...

Q3 Suppose X1, X2, ..., Xn are i.i.d. Poisson random variables with expected value ). It is well-known that X is an unbiased estimator for l because I = E(X). 1. Show that X1+Xn is also an unbiased estimator for \. 2 2. Show that S2 (Xi-X) = is also an unbaised esimator for \. n-1 3. Find MSE(S2). (We will need two facts) E com/questions/2476527/variance-of-sample-variance) 2. Fact 2: For Poisson distribution, E[(X – u)4] 312 + 1. (See for...

Let X1, . . . , Xn be i.i.d. from N(µ1, σ2 ), and Y1, ....

Let X1, . . . , Xn be i.i.d. from N(µ1, σ2 ), and Y1, . . . , Ym be i.i.d. from N(µ2, σ2 ). If the two samples are independent, find the maximum likelihood estimates for µ1, µ2, and the common variance σ 2 .