#4: Suppose that X1,... , X7n is an i.i.d. random sample drawn from a U[a, 1] uniform distribution,where 0a < 1. Suppose that you want to find an unbiased estimator, â, for a.(a) By definition, what relation must be satisfied for â to be an unbiased estimator of a(b) Use the first-order statistic to find an unbiased estimator of a. Recall that the first-orderstatistic has the p.d.f:п-1g(yn)nf(yn) f(x)daУпwhere f is the p.d.f. of each of the X;'s.(c) Find an alternative unbiased estimator â of a, which is still based on the random sample(hint: think of a common statistic we calculate from the random sample)

Part (a):Suppose α is a population parameter, then an unbiased estimator of α must satisfy the…

Answered: #4: Suppose that X1,... , X7n is an…

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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Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
3. Let X1,X2, ..,X, be a random sample form a normal distribution with E(X;) = µ;and Var(X;) = o². Assume s? = E(X;_ X)²/n and s3 = (n/(n – 1))s?. Questions: a. Compare between the estimators si and s?. b. Which one you preferred? What is (are) your reason(s). 4. Let X1,X2, . X, be a random sample form a uniform distribution, f(X)e = 0*(1– e)!-*; 0 < x < 1. Assume T1 = X1 and T, = (-)Ex;. %3D a. Check the unbiasedness property for T1 and T,. b. Find the MSE of T, and T,. Can you preferer one of them? Discuss your reasons. с. 5. Suppose that X, X2,. , X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+ X8); -1< X <1. Show that 3x is a consistent estimator of e.
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the data support the claim that the average ACT composite score of students from this students is randomly selected from a local high school with an X = 23 and s = 5.2. Do ACT composite scores are normally distributed with a u = 21. A sample of 25 students is randomly selected from a local high school with an X= 23 and s =5.L.D high school is different than 21 on the ACT composite score, using x = .05?
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