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The random variable X is distributed with pdf fX(x, θ) = (2/θ^2)*x*exp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdf fX(x, θ) = (2/θ^2)*x*exp(-(x/θ)2), where x>0 and θ>0. Please note the term within the exponential is -(x/θ)^2 and the first term includes a θ^2.

a) Find the distribution of Y = (X1 + ... + Xn)/n where X1, ..., Xn is an i.i.d. sample from fX(x, θ). If you can’t find Y, can you find an approximation of Y when n is large?

b) Find the best estimator, i.e. MVUE, of θ?

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