Define MOM estimators in each of the following cases. Are estimators consistent? Are they asymptotically normal? (a)

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Define MOM estimators in each of the following cases. Are estimators consistent? Are they asymptotically normal?

(a) Estimating \(\mu\) and \(\sigma^{2}\) based on a random sample from a normal population distribution.

(b) Estimating \(\alpha\) and \(\beta\) based on a random sample from a Beta population distribution.

(c) Estimating \(p\) based on a random sample from a geometric population distribution.

(d) Estimating \(a\) and \(b\) based on a random sample from a continuous uniform population distribution.

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