Let X₁,..., Xn be a random sample from an exponential distribution with the probability density function fx(x) = 1e-/8, for x > 0, and zero е B elsewhere. Which statement is correct. (1) X² is a consistent estimator of 3². Ă² is an unbiased estimator of 3². (III) X(1 + X) is an unbiased estimator of B² (IV) All of the above. O (1) (111) O (11) O (IV)

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[STATISTICS] MULTIPLE CHOICE Which option is correct? I will upvote the solution. Thanks!
Let X₁,..., Xn be a random sample
from an exponential distribution with the
probability density function
fx(x) = 1e/3, for a > 0, and zero
B
elsewhere. Which statement is correct.
(1) X² is a consistent estimator of 3².
(II) ² is an unbiased estimator of 3².
(III) X(1 + X) is an unbiased estimator of
3².
(IV) All of the above.
) (1)
O
(111)
O (11)
O (IV)
Transcribed Image Text:Let X₁,..., Xn be a random sample from an exponential distribution with the probability density function fx(x) = 1e/3, for a > 0, and zero B elsewhere. Which statement is correct. (1) X² is a consistent estimator of 3². (II) ² is an unbiased estimator of 3². (III) X(1 + X) is an unbiased estimator of 3². (IV) All of the above. ) (1) O (111) O (11) O (IV)
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