Find sufficient statistics for the parameters

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Reference no: EM13972897

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.

Reference no: EM13972897

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