Problem 2: If x1 is a value from a random sample from a population having auniform density with a =0 and B 0, find k so that0 0 kxiis a (1 -a) 100% confidence interval for 0

The probability distribution function can be written as follows:

Answered: Problem 2: If x1 is a value from a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Example 12.5 Two samples of sizes 40 and 50, respectively, are taken from a population with unknown mean μ and unknown variance o². Sample I: n₁ = 40, Σf x₁ Σ+ x = 16329 Sample II: n₂ = 50, Σf x₂ = 977, Σf x = 19177 Using the data from the two samples, obtain the best estimates of u and o². = 807,
This is a Statistics problem. Please explain each step thoroughly. The problem I'm having issues with is shown below:
1) Suppose tha Y is a random variable having an gamma distribution with a = 1, find the value of k such that an interval from 0 to ky is a (1 - a) 100% confidence interval for the parameter B.
Problem 3. For i = 1,2, let X;,1,.. , Xị,n, consistute a sample of size n; from a population having unknown mean u and known variance of. For X; = +E, Xij, i = 1,2, a biostatistician suggests that the "optimal" estimator of the unknown parameter u is u = wiX1+ W2X2, where the weights are chosen so that the following two conditions are simultaneously satisfied: • E[f] = 4, i.e., the estimator is unbiased • Varſi), the variance of the estimator, is minimized. Derive explicit expressions for the particular choices of wi and wz that simultaneously satisfy these two conditions, and then interpret your findings.
2 This is a more general version of Problem C.1. Let Y1, Y2, ..., Y, be n pairwise uncorrelated random variables with common mean m and common variance o. Let Y denote the sample average. (i) Define the class of linear estimators of u by W. = a,Y, + a,Y, + ..+ a,Y. where the a, are constants. What restriction on the a, is needed for W to be an unbiased estimator of u? (ii) Find Var( W.). Math Refresher C Fundamentals of Mathematical Statistics 745 For any numbers a1, az, ..., a, the following inequality holds: (a, + a, + ... + a,}/n s a + a + + a. Use this, along with parts (i) and (ii), to show that Var( Wa) = Var(Y) whenever W is unbiased, so that Y is the best linear unbiased estimator. [Hint: What does the inequality become when the a, satisfy the restriction from part (i)?] (iii)
c,d,e
6. For a left-tailed test when n = 8 and a = 0.10 the critical value is %3D a. 1.397 b. -1.397 C. 1.415 d. -1.415
Example 12.5 Two samples of sizes 40 and 50, respectively, are taken from a population with unknown mean μ and unknown variance o². Sample I: n₁ = 40, Σf x₁ Σ+ x = 16329 Sample II: n₂ = 50, Σf x₂ = 977, Σf x = 19177 Using the data from the two samples, obtain the best estimates of u and o². = 807,
Questions 1 and 2 1. A sample of n = 4 scores has SS = 60. What is the variance for this sample? 2. True or False? For a one-tailed test evaluating at treatment that is supposed to decrease scores, a researcher obtains t(8) = -1.90. For alpha = .05, the correct decision is to reject the null hypothesis.
We test the null hypothesis Ho:μ = 10 against the alternative Ha:μ<10 for a normal population with σ = 4. A random sample of 16 observations is drawn from the population, and we find the sample mean of these observations to be x̅ = 12. The P-value is?
Example 9-30. The daily consumption of milk in a city, in excess of 20,000 litres, is 1 approrimately distributed as a Gamma variate with parameters a = and A = 2- The 10,000 city has a daily stock of 30,000 litres. What is the probability that the stock is insufficient on a particular day ?
Q.2 Find the value of a when Z is a standard normal random variable and P{-3

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Problem 2: If x1 is a value from a random sample from a population having a uniform density with a = 0 and B 0, find k so that 0 0 kxi is a (1 -a) 100% confidence interval for 0