Consider an exponentially distributed random sample X1, . . . , Xn ∼ Exp(λ). (a) Give the definition of the sample mean

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Consider an exponentially distributed random sample X1,
. . . , Xn ∼ Exp(λ).
(a) Give the definition of the sample mean estimator and sample
variance estimator. [3]
(c) Give the definition of an unbiased estimator, and show that
the sample mean estimator is unbiased for θ = 1/λ. [5]
(d) State the central limit theorem (proof not required).
[4]
(e) Determine the Gaussian distribution that may be used to
approximate the sampling distribution of the sample mean estimator
for the exponential statistical