#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-order statistic has the p.d.f: п-1 g(yn)nf(yn) f(x)da Уп where 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)
#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-order statistic has the p.d.f: п-1 g(yn)nf(yn) f(x)da Уп where 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)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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![#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-order
statistic has the p.d.f:
п-1
g(yn)nf(yn) f(x)da
Уп
where 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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0185b29e-4319-418a-9d17-56f7e781125e%2Fea943d12-17ed-4bec-a62e-2e474f3a607f%2F0nidgrj.png&w=3840&q=75)
Transcribed Image Text:#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-order
statistic has the p.d.f:
п-1
g(yn)nf(yn) f(x)da
Уп
where 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)
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