If X1 and X2 are independent random variables having binomial distributions with the parameters theta and n1 and theta and n2, is (X1 + 2X2)/(n1 + 2n2) a sufficient estimator of theta?
I don't know how to approach this
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If X1 and X2 are independent random variables having binomial distributions with the parameters theta and n1 and theta and n2, is (X1 + 2X2)/(n1 + 2n2) a sufficient estimator of theta?
I don't know how to approach this
Let's see your joint distribution function. Next use the factorization theorem.