#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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2.2. Let Y₁, Y₂Yn denote a random sample from a gamma distribution with each Y-gamma (0; B) with known. Find a sufficient statistic for 8.
Let X1, X2, *. Xn be a random sample of size n from norm population with mean and unknown a. Let X and s be the sample mean and sample standard deviation. Then for any 0
H. Let X1,..., X, be a random sample from some distribution with unknown u. It's known that X 100 and X = 1783. %3D %3D (40) Supposen = 144 and o? = 12. The value of a, corresponding to the confidence interval [0.7, 1.3] is (a) 0.212 (b) 0.122 (c) 0.050 (d) 0.298
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.
You wish to test the following claim (Ha) at a significance level of a = 0.002. Ho: P1 = P2 Ha:P₁ > P2 = You obtain 48% successes in a sample of size n₁ = 790 from the first population. You obtain 43.9% successes in a sample of size n2 645 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion. O…
25. Each of a random sample of 30 student nurses who participated in a research project was given a test designed to measure the degree of creative thinking. The standard deviation of the scores was 11. Can one conclude from these data that the population variance is less than 400? Let α = 0. 05 and assume that the population is normally distributed. (A) Yes (B) No
Pls solve it quickly..
need answer of all parts in details. your answer will be appreciated.
I just need help with (d) and (e)
3. Let X, X2, .. X5, be a random sample from a population having mean u and variance o?, and let ô, =(x, + X, + X, + X,) and ô, =(2x, + X, + X, - X,) be two estimates of u. * Which of these two estimators is unbiased? * Which is the better estimator, and why? %3D
Q9. Let X,, X2, .., X, be a random sample a gamma distribution with a= 3 and B = 0>0, i.e., ..... with population p.d.f. f(x; 0) =x?e. Show that I. the MLE of e is ên = X/3. II. ê = X/3 is unbiased estimator of 0. III. ê = X/3 is MVUE of 0. %3D
(c) Which estimator, Ô, or Ö, is a more efficient estimator of 0? Explain your answer.

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