Thank you Let Y1 Yn be a random sample iid from a common den

Let Y1,..., Yn be a random sample (iid) from a common density f(y; theta) = theta y^theta-1. What is the joint density/ likelihood? What is the log-likelihood? Use these to found the mle estimator of theta (call it thetaMLE.) What is the method of moments estimator for theta? Call it theta mom Show that the information for theta in one data point (I/(theta)) is theta^-2. What is the information in all the data for theta? What is the Cramer-Rao lower bound for an unbiased estimator of theta? What is a sufficient statistic for theta? Are theta MLE and theta MOM functions of this sufficient statistic?

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