Assume that x,, . .. , Xn are the realization of the random samples X, ... , Xnwith pdf or pmf fo. Find the UMP of Ho : 0 = 0 versus H, : 0 = 0, . for0, > 0ofe(x) is density of normal with mean 0 and known o.fe(x) is density of normal with known mean u and variance 0 = o² .

Answered: Image /qna-images/answer/fcad48b1-d43f-4449-8faf-a600d9f345b0.jpg

Answered: Assume that x1, . . . , Xn are the…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

See similar textbooks

Similar questions

Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.
Consider the one-way analysis of variance model Xij = µ + a; + Eij, i= 1,.., m, j= 1,..., ni, where ɛij ~ N(0,0²) are independent. Let n= n1 + · ·+ nm, ... ni 1 ni 1 X;. >Xii for i = 1,..., m, and X. = - ΣΣΧ. ni j=1 i=1 j=1 (a) Show that SS(TO) = SS(T) + SS(E), where SS(TO) = E E i=12j=1 (Xij – X..)², m m ni SS(T) Σι (X.-Χ.) and SS(E) -ΣΣ (Χ- X.) . i=1 i=1 j=1
please make sure to answer questions b,e,f
If X is a Gaussian random variable with mean zero and variance oʻ, find the pdf of Y = \X\.
Answer 1 only
9.12 question attached
Please fast answer and correct answer
5. Let Z be a standard normal random variable. Obtain moment generating function (mgf) of Z.Find the density of random variable Y = Z2 and verify that it is a pdf.
5. Y1, Y2,..., Yn are iid normal (u, o²) where o² unknown (п-1)52 Show that is a pivot quantity for estimation of o?
5. Assume you are shooting at a target centred at the origin (0,0), but bullets land at a random point with horizontal (X) and vertical (Y) coordinates following in- dependent standard Normal (0,1) distributions. Define the distance from the tar- get to be D = VX²+Y². For independent standard Normals, we already know that X? - x²(1) = Gamma(1/2,1/2) and X² + Y² ~ x²(2) = Gamma(1, 1/2). Y /D %3D (a) Find the probability that a bullet lands in the top right quadrant. (Hint: You don't need to calculate any integrals.) (b) Find the conditional probability that a bullet lands more than 1 unit away from the centre (D > 1), given Y = X, i.e. the bullet lands on the identity line; express the probability as a function of the standard Normal CDF ¤(·). (c) Find the CDF of X² + Y² in closed form. (d) Find the probability that a bullet lands more than 1 unit away from the centre, P(D> 1). (e) Find the CDF of D based on the CDF of X? + Y². (f) Use your answer in the previous part to find the PDF of…
4
Suppose data are positive numbers a1, 2, . .., T, and suppose it is decided to model these by i.i.d. random variables X1, X2, ..., X, with common Gamma(v, A) distribution as described in Definition 3.12 of the notes. Here the shape parameter v is supposed to be known, but the rate parameterdE (0, 00) is unknown and needs to be estimated. Let Å be the MLE for A. Setting i = , e;, which of the following statements is true? O i=7/v. O If Z is defined by substituting X; for æ; in A, then Z1 has a Gamma(nv, A) distribution. O If Z is defined by substituting X; for a; in Ä, then Z-1 has a Gamma(nv, nvd) distribution. O If Z is defined by substituting X; for æ; in A, then Z has a Gamma(nv, A/(nv)) distribution. O Â=v/T. O î = (2)". O If Z is defined by substituting X; for æ; in A, then Z has a Gamma(nv, X) distribution.

SEE MORE QUESTIONS

Recommended textbooks for you

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt