Consider a random sample of size one (n 1) from the distribution with probabilityfunctionSoy(-1), if 00f(y; 0)=10.otherwise.(a) To test Ho: 0 = 0o versus H₁ : 0 = 0 > 00, find a most powerful test. Let thepositive constant to define the rejection region of the test be k.(d) Graph the power function against for k= 0.3, 0.5, 0.8, and comment on how thepower of the test changes as the values of k and change.(e) Is the above test in part (a) a uniformly most powerful test? Justify your answer.

Answered: Image /qna-images/answer/e62b6c31-9ecc-478e-b014-5ea09a577f92.jpg

Answered: Consider a random sample of size one (n…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
The differentiation approach to derive the maximum likelihood estimator (mle) is not appropriate in all the cases. Let X₁, X2,,X₁ be a random sample of size n from the population of X. Consider the probability function of X fe-(2-0), if 0
Please provide only typed answer solution no handwritten solution needed allowed
If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!
Assume that n independent count variables {X,,X2,...,X,} are identically distributed as X, ~ Poi(0) where i= 1,2,...,n and to estimate E(X,)= 0, consider the sample mean estimator ô = -5x,. n (b) Use the expectation of the distribution of S = nô to compute the expectation E(@) and the bias of this estimator. State whether this estimator unbiased. (c) Use the variance of the distribution of S= nô to examine var(Ô) and the standard error of this estimator. Use the variance and the bias of ê to compute the Mean Squared Error (MSE) of this estimator. Comment on the MSE behaviour in the asymptotic limit as n→o. State whether this estimator is consistent or (d) not.
Q3/ If the M.g.f. of random variable x is : M(t) = (0.75 + 0.25 e')" x = 0,1, 2,3, .,n 1- if (n = 4) find the Median and Pr(0 sx< 1)? 2-if (n = 5) find var(x), E X(X – 1) ? 3- find c .d. f. of X?
Suppose we collect n samplesX1,X2, . . . ,Xn from a uniform distribution U[θ,1]. We know the maximum likelihood estimator of θ is θ = min(Xi). (1) What is the CDF of θ? (2) What is the pdf of θ? (3) Find the bias of θ. (4) Find the variance of θ. (5) Find the MSE of θ.
A variable X has a probability function f(x, 0) = 0e 0x; x≥0 y >0. The parameter 0 is estimated using two different estimators of simple random samples of size two: 01 2x+4x2 and 2=4x+5x2 3 3 Select the best estimator for \theta by comparing the Mean Squared Errors
The distribution of the random variable X is a given by a function:f(x) = 1/c ; 0<x<1, = x/3 ; 1<=x < 2, = 0 ; else Determine the F(x) Count P(X > 1,4)
The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular construction supply company in a given week is a continuous random variable X with PDF as '3 - x²) 0sx <1 f(x) =2 %3D elsewhere Find the expected value and standard deviation of the amount of gravel sold in a week, a) Consider a normally distributed random variable X with a mean of 85 and standard deviation of 10. Find P(90 < X< 100)?

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS