Any ideas Suppose Y1 Y2 Yn are random variables from a distr

Any ideas?

Suppose Y_1, Y_2,..., Y_n are random variables from a distribution with the following density function Using factorization of the likelihood to show that If theta is known, find a sufficient statistic for alpha; If alpha is known, find a sufficient statistic for theta. If alpha is known, find the minimum variance unbiased estimator (MVUE) for theta. If both alpha and theta are unknown, find the method of moment estimator (MME) for theta and alpha. If both alpha and theta are unknown, find the method of moment estimator (MME) for log theta and log alpha.

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