Let Y1, Y2, . . ., Yn be a random sample from a Laplace distribution with density function
f(y|θ) = (1/2θ)e-|y|/θ for -∞ < y < ∞
where θ > 0. The first two moments of the distribution are E(Y) = 0 and E(Y2) = 2θ2.
a) Find the likelihood function of the sample.
b) What is a sufficient statistic for θ?
c) Find the maximum likelihood estimator of θ.
d) Find the maximum likelihood estimator of the standard deviation of the double exponential distribution.
e) Find the method of moments estimator of θ.
f) Show the maximum likelihood estimator is a MVUE of θ.
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