let x1.........xn be independent where xi is normally distributed with unknown mean u and unknown variance 0...

Question

Question

let x1.........xn be independent where xi is normally distributed with unknown mean u and unknown variance $\sigma 2\geq$ 0

find the UMP test for testing $\mu$ =0 against $\mu$ $\mu \geq$ 0 when it is assumed that $\sigma 2$ is known. $\sigma 2$ =1

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Add a comment

Answer 2

Similar Homework Help Questions

Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following...

Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following is sucient to conclude that the estimator T = f(X1,...,Xn) of a parameter ✓ is consistent (fully justify your answer): (a) Var(T)= (b) E(T)= and Var(T)= . (c) E(T)=. (d) E(T)= and Var(T)= We were unable to transcribe this imageWe were unable to transcribe this imageoe We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...

Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about . For testing H0: = 10 vs H1: < 10, consider the statistic T- = Ri+ (1-i), where i =1 if Xi>10 , 0 otherwise; and Ri+ is the rank of (Xi - 10) among |X1 -10|, |X2-10|......|Xn -10|. 1. Find the null mean and variance of T- . 2. Find the exact null distribution of T- for n=5. We were unable to transcribe this imageWe were...
Let X1,X2,...,Xn denote independent and identically distributed random variables with mean µ and variance 2. State...

Let X1,X2,...,Xn denote independent and identically distributed random variables with mean µ and variance 2. State whether each of the following statements are true or false, fully justifying your answer. (a) T =(n/n-1)X is a consistent estimator of µ. (b) T = is a consistent estimator of µ (assuming n7). (c) T = is an unbiased estimator of µ. (d) T = X1X2 is an unbiased estimator of µ^2. We were unable to transcribe this imageWe were unable to transcribe...

Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs...

Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs , xi > 0, where λ is fixed but unknown. Let . Here we have a relative large sample size n = 100. (ii) Notice that the population mean here is µ = E(X1) = 1/λ , population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the sample standard deviation s = 10, sample average = 5, construct a 95% large-sample approximate confidence...
Let X1,... , Xn be a random sample from the Pareto distribution with pdf { f (r0)= 0, where 0>0 is unknown (a) Find...

Let X1,... , Xn be a random sample from the Pareto distribution with pdf { f (r0)= 0, where 0>0 is unknown (a) Find a uniformly most powerful (UMP) test of size a for testing Ho 0< 0 versus where 0o>0 is a fixed real number. (Use quantiles of chi-square distributions to express the test) (b) Find a confidence interval for 0 with confidence coefficient 1-a by pivoting a ran- dom variable based on T = log Xi. (Use quantiles...
Suppose that Xi, X2, ....Xn is an iid sample from where θ 0 is unknown. (a) Find the uniformly mi...

Suppose that Xi, X2, ....Xn is an iid sample from where θ 0 is unknown. (a) Find the uniformly minimum variance unbiased estimator (UM VUE) of (b) Find the uniformly most powerful (UMP) test of versuS where θο is known. (c) Derive an expression for the power function of the test in part (b) Suppose that Xi, X2, ....Xn is an iid sample from where θ 0 is unknown. (a) Find the uniformly minimum variance unbiased estimator (UM VUE) of...

Let X1,, Xn be independent and identically distributed random variables with unknown mean μ and unknown...

Let X1,, Xn be independent and identically distributed random variables with unknown mean μ and unknown variance σ2. It is given that the sample variance is an unbiased estimator of ơ2 Suggest why the estimator Xf -S2 might be proposed for estimating 2, justify your answer
Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix...

Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix shown below: . (a) What is the probability distribution function of joint Gaussian ? (Show it with and ) (b) What is the eigenvalues of co-variance matrix ? (c) Given the condition that the sum of squared values of each eigenvector are equal to 1, what is the eigenvectors of co-variance matrix ? please help with all parts! thank you! X1 We were unable...
4. Suppose X1, . . . ,X, are independent, normally distributed with mean E(Xi) and variance...

4. Suppose X1, . . . ,X, are independent, normally distributed with mean E(Xi) and variance Var(X)-σί. Let Żi-(X,-μ.)/oi so that Zi , . . . , Ζ,, are independent and each has a N(0, 1) distribution. Show that LZhas a x2 distribution. Hint: Use the fact that each Z has a xî distribution i naS

(5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the...

(5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the distributions of each of V and W. (b) Find E(V) and E(W) (5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the distributions of each of V and W. (b)...

let x1.........xn be independent where xi is normally distributed with unknown mean u and unknown variance 0...

Homework Answers

Add Answer to:
let x1.........xn be independent where xi is normally distributed with unknown mean u and unknown variance 0...

Post as a guest

Earn Coins

Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following...

Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...

Let X1,X2,...,Xn denote independent and identically distributed random variables with mean µ and variance 2. State...

Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs...

Let X1,... , Xn be a random sample from the Pareto distribution with pdf { f (r0)= 0, where 0>0 is unknown (a) Find...

Suppose that Xi, X2, ....Xn is an iid sample from where θ 0 is unknown. (a) Find the uniformly mi...

Let X1,, Xn be independent and identically distributed random variables with unknown mean μ and unknown...

Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix...

4. Suppose X1, . . . ,X, are independent, normally distributed with mean E(Xi) and variance...

(5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the...

let x1.........xn be independent where xi is normally distributed with unknown mean u and unknown variance 0...

Homework Answers

Add Answer to: let x1.........xn be independent where xi is normally distributed with unknown mean u and unknown variance 0...

Post as a guest

Earn Coins

Add Answer to:
let x1.........xn be independent where xi is normally distributed with unknown mean u and unknown variance 0...