Problem 1:
Consider a sample from the pdf
f(x) = 1/θ exp{-(x - θ)/θ}, x > θ,
where θ > 0 is a parameter.
1. Find an estimator of the parameter using the method of moments.
2. Find a sufficient statistic for the parameter.
Problem 2:
Consider a sample from the pdf
f(x) = [λ/2Πx3]1/2 exp{-λ(x - μ)2/2μ2x}, x > 0,
where λ > 0 and μ > 0 are parameters.
1. Find an estimator of the parameters using the method of moments.
2. Find sufficient statistics for the parameters.