8.19 Suppose that Y₁, Y2, . . ., Y, denote a random sample of size n from a population with an exponential distribution whose density is given by (1/0)e-y/0, f(y) = 0, y > 0, elsewhere. If Y(1) = min(Y₁, Y2, ..., Yn) denotes the smallest-order statistic, show that Ô = nY (1) is an unbiased estimator for and find MSE(Ô). [Hint: Recall the results of Exercise 6.81.]

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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Question 8.19 from Mathematical statistics with applications (Wackerly):

8.19
Suppose that Y₁, Y2, . . ., Y, denote a random sample of size n from a population with an
exponential distribution whose density is given by
(1/0)e-y/0,
f(y)
=
0,
y > 0,
elsewhere.
If Y(1)
=
min(Y₁, Y2, ..., Yn) denotes the smallest-order statistic, show that Ô = nY (1) is an
unbiased estimator for and find MSE(Ô). [Hint: Recall the results of Exercise 6.81.]
Transcribed Image Text:8.19 Suppose that Y₁, Y2, . . ., Y, denote a random sample of size n from a population with an exponential distribution whose density is given by (1/0)e-y/0, f(y) = 0, y > 0, elsewhere. If Y(1) = min(Y₁, Y2, ..., Yn) denotes the smallest-order statistic, show that Ô = nY (1) is an unbiased estimator for and find MSE(Ô). [Hint: Recall the results of Exercise 6.81.]
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